WATER  POWER  ENGINEERING 


THE  THEORY,  INVESTIGATION  AND  DEVELOPMENT 
OF  WATER  POWERS. 


BY 

DANIEL  W.  MEAD. 

Member  American  Society  Civil  Enginet 

Consulting  Engineer 

Professor  of  Hydraulic  and  Sanitary  Engineering 
University  of  Wisconsin 


NEW    YORK 

McGRAw  PUBLISHING  Co. 
1908 


GENERAL 


Copyrighted  1907-1908 


BY 


DANIEL  W.  MEAD 


STATE  JOURNAL  PRINTING  COMPANY 
MADISON,  WISCONSIN 


A 


PREFACE 


In  the  development  of  a  water  power  project  the  engineer  is  fre- 
qently  called  upon  to  do  more  than  design  and  construct  the  power 
plant.  He  may  be  required  to  report  on  the  adequacy  of  the  supply, 
the  head  and  power  available  and  the  probable  variations  in  the 
same,  the  plan  for  development,  the  cost  of  construction  and  opera- 
tion, and  the  advisability  of  the  investment.  A  study  of  the  entire 
project,  therefore,  becomes  essential,  and  each  factor  must  be  care- 
fully considered  in  detail  to  assure  ultimate  success.  Each  of  the 
features  of  the  development  is  of  equal  importance  to  the  commer- 
cial success  of  the  project.  The  majority  of  the  failures  in  water 
power  development  have  occurred  from  causes  other  than  structural 
defects,  and  a  knowledge  of  these  other  important  and  controlling- 
factors  is  therefore  quite  as  essential  as  a  knowledge  of  design  and 
construction.  It  must  be  said,  however,  that  in  respect  to  some  of 
these  controlling  factors  current  practice  has  not  been  what  it  should 
be.  This  has  resulted  in  many  over-developments  and  illy  advised 
installations,  from  which  the  power  generated  has  not  been  equal 
to  tfiat  anticipated,  and  in  many  poor  financial  investments  amount- 
ing frequently  to  practical  failures.  The  engineer  has  given  much 
attention  to  design  and  construction  but  too  little  attention  to  the 
other  fundamental  considerations  mentioned  above  on  which  the 
success  of  the  project  depends  to  an  equal  extent. 

In  the  preparation  of  this  book  the  author  has  endeavored  to  con- 
sider, briefly  at  least,  all  fundamental  principles  and  to  point  out  the 
basis  on  which  successful  water  power  development  depends.  The 
method  of  study  and  investigation  outlined  herein  was  developed  by 
the  author  during  twenty-five  years  of  professional  practice  and  in 
his  efforts  to  illustrate  the  principles  underlying  the  subject  in  his 
lectures  to  the  senior  class  in  water  power  engineering  at  the  Uni- 
versity of  Wisconsin.  A  somewhat  extended  acquaintance  with  the 
literature  relating  to  water  power  engineering  leads  the  author  to 
believe  that  in  a  number  of  features  the  principles  and  methods  de- 
scribed in  this  book  are  somewhat  in  advance  of  present  practice. 


vi  Preface. 

In  current  practice,  the  hydraulic  engineer,  to  determine  the  ex- 
tent of  a  proposed  hydraulic  development,  commonly  depends  on  a 
study  of  the  monthly  averages  of  stream  flow  and  of  observed  maxi- 
mum and  minimum  flows.  He  usually  assumes  from  his  previous 
knowledge  and  study  that  the  development  should  be  based  on  a 
certain  minimum  or  average  stream  discharge  per  square  mile  of 
drainage  area.  The  value  of  this  method  depends  on  the  breadth  of 
the  engineer's  local  knowledge  of  rainfall  and  run-off  relations. 
With  a  sufficient  knowledge  of  these  conditions,  this  method  may 
form  a  safe  basis  for  water  power  development  but  it  fails  to  give 
the  complete  information  which  is  essential  for  a  full  comprehension 
of  the  subject.  In  other  cases  the  development  is  predicted  on  a 
single,  or  on  a  very  few,  measurements  of  what  is  believed,  or  as- 
sumed to  be,  the  low  water  flow  of  the  stream.  This  method,  even 
when  accompanied  by  careful  study  of  rainfall  records,  is  a  danger- 
ous one  to  employ  as  many  over-developed  water  power  projects 
demonstrate.  Neither  of  these 'methods  compares  favorably  with 
the  more  exact  method  of  studying  flow  by  actual  or  comparative 
hydrographs  as  is  described  in  Chaps.  IV,  V,  VIII  and  IX. 

In  current  practice  the  head  available  is  usually  determined  for 
average  conditions,  or,  perhaps,  occasionally  for  low,  average  and 
high  water  conditions,  and  no  detailed  study  of  the  daily  effect  on 
power  is  attempted.  In  Chaps.  IV  and  V  this  subject  is  presented 
in  detail  and  a  method  of  the  investigation  of  this  important  subject, 
under  all  conditions  of  flow  and  all  conditions  of  use,  is  outlined. 

On  the  basis  of  the  knowledge  gained  from  the  study  of  flow  and 
head,  the  study  of  the  power  that  can  be  developed  for  each  day  in 
the  year  and  during  each  year  for  which  actual  or  comparative  hy- 
drographs are  available,  is  outlined.  An  outline  of  a  method  for 
the  consideration  of  possible  variations  in  flow  during  periods  for 
which  no  measurements  are  available  based  on  the  available  rain- 
fall records,  is  also  given  in  Chaps.  VI,  VII  and  VIII.  A  study  of 
the  effect  of  pondage  on  power,  a  most  important  matter,  though 
not  always  carefully  considered,  or  appreciated,  is  also  discussed  in 
considerable  detail  in  Chaps.  IV,  V  and  XXVI. 

In  the  selection  of  turbines  for  a  water  power  project,  the  current 
practice  has  been  for  the  engineer,  while  drawing  certain  conclu- 
sions from  the  tables  of  manufacturers'  catalogues,  to  present  to  the 
manufacturer  the  conditions  under  which  the  power  is  to  be  devel- 
oped and  to  rely  largely  or  entirely  on  the  manufacturer  for  advice 


Preface.  vii 

as  to  machinery  to  be  used.  In  such  cases  he  is  dependent  for  re- 
sults on  guarantees  which  are  usually  quite  indefinite  in  character 
and  seldom  verified  by  actual  tests,  under  working  conditions,  be- 
fore the  wheels  are  accepted  and  paid  for.  This  has  resulted  in 
many  cases  in  the  installation  of  wheels  which  are  entirely  unsuited 
to  the  particular  conditions  under  which  they  are  installed. 

Practical  turbine  analysis  has  not  been  treated  except  in  the  most 
general  way  in  any  publications  except  the  various  German  treatises 
on  the  turbine  in  which  the  subject  is  discussed  from  the  basis  of 
turbine  design.  The  author  has  developed  the  method  of  turbine 
analysis  and  selection,  outlined  in  Chapters  XIV  and  XVI, 
which  applies  to  all  wheels  when  tests  of  wheels  of  the  series  or 
class  considered  are  available.  These  methods  are  based  on  the 
practical  operating  conditions  of  actual  tests  and  are  both  theoreti- 
cally and  practically  correct.  The  engineer  should  be  able  to  intel- 
ligently select  the  turbines  needed  for  the  particular  conditions  of  his 
installation  and  to  determine,  with  a  considerable  degree  of  accuracy, 
the  results  on  which  he  can  depend  during  all  conditions  of  head 
and  flow. 

It  is  believed  that  this  treatment  of  the  subject  is  sufficiently 
complete  to  place  the  selection  of  turbines  on  a  better  footing  and 
that,  when  adopted,  it  will  lead  to  the  selection  of  better  and  more 
improved  designs  and  assure  more  satisfactory  results. 

The  subject  of  turbine  governing  has,  for  electrical  reasons,  be- 
come an  important  one.  While  a  number  of  important  papers  have 
appeared  on  this  subject,  there  is,  so  far  as  the  author  knows,  no 
discussion  in  English  which  offers  the  engineer  a  basis  for  a  com- 
plete consideration  of  this  subject.  Chap.  XVIII,  on  the  principles 
of  turbine  governing  together  with  appendixes  A,  B  and  C,  offer, 
it  is  believed,  suggestions  for  the  consideration  of  this  subject  which 
may  prove  of  value  to  water  power  engineers. 

The  report  on  a  water  power  project  should  involve  a  careful 
and  complete  investigation  of  the  entire  subject,  and  should  be 
based  on  the  broadest  considerations  of  the  project  in  all  its  rela- 
tions. Many  reports  which  have  come  to  the  author's  attention 
have  been  too  limited  in  scope  and  have  included  only  general  opin- 
ions which  have  not,  to  his  mind,  been  sufficiently  specific  or  based 
on  sufficient  information  to  warrant  approval  without  extended  in- 
vestigations. In  Chap.  XXVIII  the  author  has  outlined  his  idea 


viii  Preface. 

of  the  extent  and  scope  of  such  investigation  and  report,  which  he 
believes  is  essential  for  an  intelligent  investigation  and  a  reliable 
opinion  on  this  subject. 

ACKNOWLEDGMENTS. 

There  can  be  little  which  is  strictly  new  or  original  in  any  technical 
work,  and  in  offering  this  book  to  the  profession,  the  author  wishes  to 
acknowledge  his  indebtedness  to  the  large  number  of  technical  ar- 
ticles that  have  already  appeared  on  various  phases  of  the  subject. 
Many  references  to  such  literature  have  been  given  at  the  end  of  the 
various  chapters. 

Many  illustrations  have  been  taken,  with  more  or  less  change 
from  Engineering  News,  Engineering  Record,  Cassier's  Magazine 
•and  Electrical  World  and  Engineer.  Various  manufacturers  have 
furnished  photographs  and,  in  some  cases,  cuts  of  their  wheels,  gov- 
ernors and  apparatus,  in  connection  with  which  their  names  appear. 

The  author  has  been  greatly  aided  by  his  assistants,  both  of  his 
own  private  office  and  of  the  University  staff.  He  wishes  especially 
to  acknowledge  the  assistance  of  Mr.  L.  F.  Harza  to  whom 
Chap.  XVIII  on  The  Speed  Regulation  of  Turbine  Water  Wheels 
and  appendixes  A,  B  and  C  are  largely  due.  Mr.  Harza  has  also 
been  of  much  assistance  in  the  editorial  work  of  publication.  Es- 
pecial acknowledgment  is  also  due  to  Professor  G.  J.  Davis,  Jr., 
for  the  preparation  of  the  diagrams  of  friction  of  water  in  pipes  and 
of  Bazin's  and  Kutter's  coefficients,  etc.  Mr.  Robert  Ewald  assisted 
in  the  selection  of  material  for  illustrations,  in  the  investigation  of 
German  literature,  and  the  preparation  of  various  graphical  diagrams, 
including  the  first  development  of  the  characteristic  curve. 

The  author  also  desires  to  acknowledge  his  indebtedness  to  his 
principal  assistant,  Mr.  C.  V.  Seastone,  for  advice  and  assistance  in 
the  arrangement  of  many  of  the  chapters  in  this  work  and  assist- 
ance in  the  editorial  work  of  publication. 

The  sources  of  various  other  tables,  illustrations,  etc.,  are  ac- 
knowledged in  their  proper  places.  D.  W.  M. 

Madison,  Oct.  i,  1908. 


CONTENTS 


CHAPTER  I. 
INTRODUCTION. 

The  History  of  Water  Power  Development— Every  Development  of 
Water  Power — The  Earliest  Type  of  Water  Wheel — The  Undershot 
Wheel — The  Overshot  and  Breast  Water  Wheel — The  Development 
of  the  Turbine — Fundamental  Ideas  of  the  Turbine — The  Modern 
Turbine. — The  American  or  Francis  Turbine — Modern  Changes  in 
Turbine  Practice — Historical  Notes  on  Water  Power  Development — 
Development  of  Water  Power  in  the  United  States — Literature 1 

CHAPTER  II. 

POWEB. 

The  Development  of  Potential  Energy— Definition  of  Energy — Solar 
Energy  the  Ultimate  Source — No  Waste  of  Energy  in  Nature — Laws 
of  Energy  Conservation — Efficiency — Natural  Limit  to  Efficiency — < 
Practical  Limits  to  Efficiency— Efficiency  of  a  Combined  Plant — 
Capacity  of  Each  Part  of  a  System  not  Identical — The  Analysis  of 
Losses — The  Losses  in  a  Hydro-Electric  Plant — Units  of  Energy- 
Conversion  of  Energy  Units — Kinetic  Energy — Uniform  Motion — 
Uniform  Varied  Motion— Compound  Motion, — Graphical  Representa- 
tion of  the  Laws  of  Motion — Transformation — Literature 19 

CHAPTER  III. 
HYDRAULICS. 

IBasis  of  Hydraulics — Mathematical  Expression  for  Energy— Velocity 
Head.— Entrance  Head — Submerged  Orifices — Friction  Head — Kut- 
ter's  Formula — Bazin's  Formula — Efficiency  of  Section — Determina- 
tion of  Canal  Cross-Section — The  Back  Water  Curve — Flow  of 
Water  in  Pipes— The  Flow  of  Water  Through  Orifices— Flow  over 
Weirs — Literature 40 

CHAPTER  IV. 
WATER  POWEK. 

The  Study  of  the  Power  of  a  Stream  as  Affected  by  Flow—Source  of 
Water  Power— Factors  of  Stream  Flow— Broad  Knowledge  of 


Contents. 

Stream  Flow  Necessary — The  Hydrograph — The  Use  of  Local 
Hydrographs — Use  of  Comparative  Hydrographs — Reliability  of 
Comparative  Hydrographs — When  no  Hydrographs  are  Available — 
The  Hydrograph  as  a  Power  Curve 79 


CHAPTER  V. 
WATER  POWER  (Continued) 

The  Study  of  the  Power  of  a  Stream  as  Affected  by  Head — Variations 
in  Head — The  Rating  or  Discharge  Curve— The  Tail  Water  Curve— 
The  Head  Water  Curve— Graphic  Representation  of  Head — Effects 
of  Design  of  Dam  on  Head — Effect  of  Head  on  the  Power  of  the 
Plant — Graphical  Representation  of  the  Relations  of  Power,  Head 
and  Flow — Graphical  Study  of  Power  at  Kilbourn — Power  of  the 
Kilbourn  Wheels  Under  Variations  in  Flow — Effects  of  Low  Water 
Flow — Effects  of  Number  of  Wheels  on  Head  and  Power. . .  93 


CHAPTER  VI. 
RAINFALL. 

Importance  of  Rainfall  Study — Distribution  of  Rainfall — The  Rainfall 
Must  be  Studied  in  Detail — Local  Variation  in  Annual  Rainfall.— 
Local  Variations  in  Periodical  Distribution  of  Annual  Rainfall — 
Accuracy  of  Rainfall  Maps  and  Records — Rainfall  and  Altitude — 
Value  of  Extended  Rainfall  Records — Accuracy  in  Rainfall,  Obser- 
vation,—District  Rainfall — Study  of  Rainfall  as  Affecting  Run-off — 
Literature..  Ill 


CHAPTER  VII. 
THE  DISPOSAL  OF  THE  RAINFALL. 

Factors  of  Disposal — The  Rate  or  Intensity  of  Rainfall— Condition  of 
Receiving  Surfaces  and  Geological  Strata— Effects  of  Wind — Effects 
of  Vegetation — Percolation— Evaporation — Evaporation  Relations — 
Practical  Consideration  of  Losses— Literature 133: 


CHAPTER  VIII. 
RUN-OFF. 

Run-off — Influence  of  Various  Factors — Relations  of  Annual  Rainfall 
and  Run-off  of  Wrater  Year— Relation  of  Periodic  Rainfall  to  Run- 
off— Monthly  Relation  of  Rainfall  and  Run-off — Maximum  Stream 
Flow — Estimate  of  Stream  Flow 146 


Contents. 

A.1 

CHAPTER  IX. 
RUN-OFF  (Continued) 

Relation  of  Run-off  to  Topographical  Conditions— Effects  of  Geological 
Condition  on  the  Run-off— The  Influence  of  Storage  on  the  Distri- 
bution of  Run-off—Effects  of  Area  on  the  Run-off— The  Study  of  a 
Stream  from  Its  Hydrographs— Comparative  Runoff  and  Compara- 
tive Hydrographs— Comparative  Hydrographs  from  Different 
Hydrological  Divisions  of  the  United  States,— Literature. .  175 


CHAPTER  X. 
STREAM  FLOW. 

Flow  in  Open  Channels— Changes  in  Value  of  Factors  with  Changes 
in  Flow — Effects  of  Variable  Flow  on  the  Hydraulic  Gradient- 
Effects  of  a  Rising  or  a  Falling  Stream  on  Gradient— Effects  of 
Channel  Condition  on  Gradient— Effect  of  Change  in  Grade  and  of 
Obstructions— Relation  of  Gauge  Heights  to  Flow— Variations  in 
Velocity  in  the  Cross-Section  of  a  Stream — Effects  of  Ice-Covering 
on  the  Distribution  of  Velocities 


CHAPTER  XI. 
THE  MEASUREMENT  OF  STREAM  FLOW. 

Necessity  for  Stream  Flow  Measurements— Methods  for  the  Estimate 
or  Determination  of  Flow  in  Open  Channels— Estimates  from 
Cross-Section  and  Slope — Weir  Measurement — Measurement  of 
Flow  by  the  Determination  of  Velocity — The  Use  of  the  Current 
Meter — Current  Meter  Observatons  and  Computation- — Float 
Measurements — The  Application  of  Stream  Gaugings — Literature.  218 


CHAPTER  XII. 
WATER  WHEELS. 

Classification  of  Water  Wheels — Gravity  Wheels— Reaction  Wheels — 
Impulse  Wheels — Use  of  Water  Wheels— Classification  of  Tur- 
bines— Conditions  of  Operation — Relative  Advantage  of  Reaction 
and  Impulse  Turbines — Relative  Turbine  Efficiencies — Turbine  De- 
velopment in  the  United  States — The  American  Fourneyron  Tur- 
bine— The  American  Jonval  Turbine — The  American  Type  of  Re- 
action Turbine — The  Double  Leffel  Turbine — Other  American 
Wheels — Early  Development  of  Impulse  Wheels — American  Im- 
pulse Wheels — Turbine  Development  in  Europe 237 


xii  Contents. 

CHAPTER  XIII. 
TURBINE  DETAILS  AND  APPURTENANCES. 

The  Runner — Its  Material  and  Manufacture — Diameter  of  the  Run- 
ner— The  Details  of  the  Runner — Vertical  Turbine  Bearings, — Hori- 
zontal Turbine  Bearings — Thrust — Bearing  in  Snoqualmie  Falls 
Turbine— The  Chute  Case — Turbine  Gates— The  Draft  Tube 284 

CHAPTER  XIV. 
HYDRAULICS  OF  THE  TURBINE, 

Practical  Hydraulics  of  the  Turbine — Nomenclature  Used  in  Chapter — 
First  Principles — impulse  and  Reaction — The  impulse  Wheel — 
Effect  of  Angle  of  Discharge  on  Efficiency — Reaction  Wheel — 
Graphical  Relation  of  Energy  and  Velocity  in  Reaction  Turbine- — 
Turbine  Relations — Relation  of  Turbine  Speed  to  Diameter  and 
Head — Graphical  Expression  of  Speed  Relations — Relations  of  q> 
and  Efficiency — Discharge  of  Turbine  at  Fixed  Gate  Opening, — 
Power  of  a  Turbine — The  Relation  of  Discharge  to  the  Diameter  of 
a  Turbine — The  Relation  of  Power  to  the  Diameter  of  a  Turbine — 
Relation  of  Speed  to  Discharge  of  Turbines,— Relations  of  Speed  to 
Power  of  Turbines — Value  of  Turbine  Constants — Literature....  309 

CHAPTER  XV. 
TURBINE  TESTING. 

The  Importance  of  Testing  Machinery — The  Testing  of  Water  Wheels — 
Smeaton's  Experiments — The  Early  Testing  of  Turbine  Water 
Wheels — The  Testing  of  Turbines  by  James  Emerson— The  Holyoke 
Testing  Flume — The  Value  of  Tests — Purpose  of  Turbine  Testing — 
Factors  that  Influence  the  Results  of  a  Test — Measurement  of  Dis- 
charge— Measurement  of  Head — Measurement  of  Speed  of  Rota- 
tion— Measurement  of  Power — Efficiency — Illustration  of  Methods 
and  Apparatus  for  Testing  Water  Wheels— Tests  of  Wheels  in 
Place — Literature 355 

CHAPTER  XVI. 
THE  SELECTION  OF  THE  TURBINE. 

Effect  of  Condtions  of  Operation — Basis  for  the  Selection  of  the  Tur- 
bine— Selection  of  the  Turbine  for  Uniform  Head  and  Power — The 
Selection  of  a  Turbine  for  a  Given  Speed  and  Power  to  Work  under 
a  Given  Fixed  Head — To  Estimate  the  Operating  Results  of  a  Tur- 
bine under  one  Head  from  Test  Results  Secured  at  Another  Head — 
To  Estimate  the  Operating  Results  of  a  Turbine  of  one  Diameter 
from  Test  Results  of  Another  Diameter  of  the  Same  Series — To 
Estimate  the  Operating  Results  of  a  Turbine  under  Variable 


Contents.  xiii 

Heads  from  a  Test  Made  under  a  Fixed  Head— A  More  Exact 
Graphical  Method  for  Calculation- — The  Construction  of  the  Char- 
acteristic Curves  of  a  Turbine — The  Consideration  of  the  Turbine 
from  its  Characteristic  Curve — Other  Characteristic  Curves — 
Graphical  Analysis  as  Proposed  by  Mr.  W  A.  Waters 384 

CHAPTER  XVII. 

THE  LOAD  CURVE  AND  LOAD  FACTORS,  AND  THEIR  INFLUENCE  ON  THE  DESIGN  OF 

THE  POWER  PLANT. 

Variation  in  Load — Load  Curves  of  Light  and  Power  Plants. — Factory 
Load  Curves — Load  Curve  of  London  Hydraulic  Supply  Company — 
Railway  Load  Curves — Load  Conditions  for  Maximum  Returns.— The 
Load  Curve  in  Relation  to  Machine  Selection — Influence  of  Manage- 
ment on  Load  Curve — Relation  of  Load  Curve  to  Stream  Flow  and 
Auxiliary  Power — Literature 420 

CHAPTER  XVIII. 
THE  SPEED  REGULATION  OF  TURBINE  WATER  WHEELS. 

The  Relation  of  Resistance  and  Speed — Self-Regulation  in  a  Plant  with 
Variable  Speed  and  Resistance — The  Relations  Necessary  for  Con- 
stant Speed — The  Ideal  Governor — Present  Status — Value  of  Uni- 
form Speed — The  Problem — Energy  Required  to  Change  the  Pen- 
stock Velocity — Hunting  or  Racing — Nomenclature — Shock  of 
Water  Hammer  Due  to  Sudden  Changes  in  Velocity — Permissible 
Rates  of  Gate  Movement — Regulation  of  Impulse  Wheels — Influences 
Opposing  Speed  Regulation,— Change  of  Penstock  Velocity — Effect 
of  Slow  Acceleration  on  Water  Supplied  to  Wheel— Value  of  Racing 
or  Gate  Over-Run — Energy  Required  to  Change  the  Penstock  Velo- 
city— Effect  of  Sensitiveness  and  Rapidity  of  Governor — The  Fly- 
Wheel — The  Stand-Pipe— The  Air  Chamber— Predetermination  of 
Speed  Regulation  for  Wheel  set  in  open  Penstocks — Predetermina- 
tion of  Speed  Regulation,  Plant  with  Closed  Penstock,— Predeter- 
mination of  Speed  Regulation,  Plant  with  Standpipe— Application 
of  Method,  Closed  Penstock — Application  of  Method,  Open  Penstock 
— Application  of  Method,  Plant  with  Standpipe — Literature 440 

CHAPTER  XIX. 
THE  WATER  WHEEL  GOVERNOR. 

Types  of  Water  Wheel  Governors— Simple  Mechanical  Governors — Anti- 
racing  Mechanical  Governors — Details  and  Applications  of  Wood- 
ward Governors — The  Lombard-Replogle  Mechanical  Governors — 
Essential  Features  of  an  Hydraulic  Governor — Details  of  Lombard 
Hydraulic  Governor— Operating  Results  with  Lombard  Governor — 
The  Sturgess  Hydraulic  Governor — Test  Results  with  Sturgess  Gov- 


xiv  Contents. 

ernor — Control  from  Switchboard — Connection  of  Governors  to 
Gates— Relief  Valves — Lombard  Hydraulic  Relief  Valves — Sturgess 
Relief  Valves 470 


CHAPTER  XX. 
ARRANGEMENT  OF  THE  REACTION  WIIKKL. 

General  Conditions — Necessary  Submergence  of  Reaction  Wheels — Ar- 
rangement of  Vertical  Shaft  Turbine — Arrangement  of  Horizontal 
Turbine?,— Classification  of  Wheels — Vertical  Wheels  and  Their  Con- 
nection— Some  Installations  of  Vertical  Water  Wheels — Some  In- 
stallations of  Vertical  Wheels  in  Series — Some  Installations  of 
Horizontal  Water  Wheels— Some  Installations  of  Multiple  Tandem 
Horizontal  Wheels — Unbalanced  Wheels  .  500 


CHAPTER  XXL 
THE  SELECTION  OF  MACHINERY  AND  DESIGN  OF  PLANT. 

Plant  Capacity — Influence  of  Choice  of  Machinery  on  Total  Capacity — 
Effect  of  Size  of  Units  on  Cost — Overload — Economy  in  Operation — 
Possibilities  in  Prime  Movers — Capacity  of  Prime  Movers — The  In- 
stallation of  Tandem  Water  Wheels — Power  Connection — Various 
Methods  of  Connection  in  Use — Use  of  Shafting — The  Wheel  Pit — 
Turbine  Support — Trash  Racks 525 


CHAPTER  XXII. 
EXAMPLES  OF  WATER  POWER  PLANTS. 

Sterling  Plant,— Plant  of  York-Haven  Water  Power  Company — Plant  of 
South  Bend  Electric  Company — Spier  Falls  Plant  of  the  Hudson 
River  Power  Transmission  Company — Plant  of  Columbus  Power 
Company — Plant  of  the  Dolgeville  Electric  Light  and  Power  Co. — 
Plant  of  the  Shawinigan  Water  and  Power  Company — Plant  of  the 
Concord  Electric  Company — Plant  of  Winnipeg  Electric  Railway 
Co. — Plant  of  Nevada  Power,  Mining,  and  Milling  Co.— Literature. .  537 

CHAPTER  XXIII. 
THE  RELATION  OF  DAM  AND  POWER  STATION. 

General  Consideration — Classification  of  Types  of  Development — Con- 
Centrated  Fall — Examples  of  the  Distribution  of  Water  at  Various 
Plants — Head  Races  only — Plants  Located  in  Dam — High  Head  De- 
velopments    561 


Contents.  xv 

CHAPTER  XXIV. 
PRINCIPLES  OF  CONSTRUCTION  OF  DAMS. 

Object  of  Construction— Dams  for  Water  Power  Purposes— Height  of 
Dam— Available  Head— The  Principles  of  Construction  of  Dams— 
The  Foundations  of  Dams — Strength  of  Dams — Flood  Flows.— Im- 
pervious Construction, — The  Stability  of  Masonry  Dams — Calcula- 
tions for  Stability — Further  Considerations — Types  and  Details  of 
Dams— Literature 579 

CHAPTER  XXV. 
APPENDAGES  TO  DAMS. 

Movable    Dams — Flood    Gates — Flash    Boards — Head    Gates    and    Gate 

Hoists — Fish  ways — Logways — Literature 603 

CHAPTER  XXVI. 
PONDAGE  AND  STORAGE. 

Effect  of  Pondage  on  Power — Effect  of  Limited  Pondage  on  the  Power 
Curve — Power  Hydrograph  at  Sterling,  Illinois — Effect  of  Pondage 
on  other  Powers— Effect  of  Limited  Storage — Effect  of  Large  Stor- 
age— Effect  of  Auxiliary  Power — Effect  of  Maximum  Storage — Cal- 
culation for  Storage — Method  of  Storage  Calculation— Analytical 
Method— Literature 624 

CHAPTER  XXVI T. 
COST,  VALUE  AND  SALE  OF  POWER. 

Financial  Consideration — Purpose  of  Development — Cost  of  Water  Pow- 
er— Depreciation — Annual  Cost  of  Developed  Power — Cost  of  Distri- 
bution— Effect  of  Partial  Loads  on  Cost  of  Power — Cost  of  Auxil- 
iary Power  or  Power  Generated  from  other  than  Water  Power 
Sources — Market  Price  of  Water  Power — Sale  of  Power — An  Equi- 
table Basis  for  the  Sale  of  Power — Value  of  Improvements  Intended 
to  Effect  Economy — Value  of  a  Water  Power  Property — Literature.  G46 

CHAPTER  XXVIII. 
THE  INVESTIGATION  OF  WATER  POWER  PROJECTS. 

The  Extent  of  the  Investigation— Preliminary  Investigation  and  Re- 
port—Study of  Run-off — Study  of  Rainfall— Study  of  Topographi- 
cal and  Geological  Conditions — Study  of  Flood-flow — Study  of 
Back  Water  Curve — Study  of  Head — Study  of  Storage  and  Pond- 
age—Study of  Probable  Load  Curve— Study  of  Power  Development 
Study  of  Auxiliary  Power— Study  of  Site  of  Dam  and  Power  Sta- 
tion— Study  of  Plant  Desigrv— The  Estimate  of  Cost— The  Report. .  675 


xvi  Contents. 

APPENDICES. 

A.  Water  Hammer — B.  Speed  Regulation,  a  more  Detailed  Analysis 
than  in  Chapter  XVIII — C.  The  Stand-Pipe — D.  Test  Data  of  Turbine 
Water  Wheels — E.  Effect  of  an  Umbrella  upon  Formation  of  Vor- 
tices— F.  Evaporation  Tables — G.  Two  New  Water  Wheel  Governors 
— H.  Miscellaneous  Tables  Including:  Equivalent  Measures  and 
Weights  of  Water — Equivalent  Units  of  Energy — Velocities  in  Feet 
per  Second  Due  to  Heads  from  0  to  50  Feet — Three  Halves  Powers 
of  Numbers,  0  to  100 — Five  Halves  Powers  of  Numbers,  0  to  50 — Re- 
lation of  mean  Rainfall  to  Maximum  and  Minimum  Discharge 
of  Various  Rivers — Rainfall,  Run-off  and  Evaporation  for  Storage, 
Growing  and  Replenishing  Periods  or  12  Streams  of  the  United 
States..  ..685-75T 


WATER  POWER  ENGINEERING. 


CHAPTER    I. 

INTRODUCTION. 

THE  HISTORY  OF  WATER  POWER  DEVELOPMENT. 

1.  Early  Development  of  Water  Power. — Most  methods  of 
power  generation  can  be  traced  to  an  origin  at  no  very  remote 
period.    Their  development  has  been  within  historic  times.    The 
first  development  of  water  power,  however,  antedates  history. 
Its  origin  is  lost  in  remote  antiquity. 

Air  and  water,  both  physical  agents  most  essential  to  life,  have 
ever  been  the  most  obvious  sources  of  potential  energy  and  have 
each  been  utilized  for  power  purposes  since  the  earliest  times. 
Beside  the  Nile,  the  Euphrates,  and  the  Yellow  Rivers,  thou- 
sands of  years  ago  the  primitive  hydraulic  engineer  planned  and 
constructed  his  simple  forms  of  current  wheels  and  utilized  the 
energy  of  the  river  current  to  raise  its  waters  and  irrigate  the 
otherwise  arid  wastes  into  fertility.  Such  primitive  wheels  were 
also  utilized  for  the  grinding  of  corn  and  other  simple  power 
purposes.  From  these  simple  forms  and  primitive  applications 
have  gradually  been  developed  the  modern  water  power  installa- 
tions of  to-day. 

2.  The  Earliest  Type  of  Water  Wheel.— The  crude  float  wheel 
driven  directly  by  the  river  current  developed  but  a  small  por- 
tion of  the  energy  of  the  passing  stream.     The  Chinese  Nora, 
built  of  bamboo  with  woven  paddles,  is  still  in  use  in  the  east 
(see  Fig.  i),  and  was  probably  the  early  form  of  development  of 
this  type  of  wheel.     The  type  is  by  no  means  obsolete  for  it  is 
yet  used  for  minor  irrigation  purposes  in  all  countries.     These 
wheels,  while  inefficient,  served  their  purpose  and  were  exten- 
sively developed  and  widely  utilized.     One  of  the  greatest  de- 
velopments of  which  there  is  record  was  the  float  wheel  installa- 


Introduction. 


Fig.    1. — Chinese   Nora   or    Float   Wheel    Used    From    Earliest   Times    to 

Present. 

tion  used  to  operate  the  pumps  at  London  Bridge  for  the  first 
water  supply  system  of  the  city  of  London,  and  constructed 
about  1581  (see  Fig.  2).  In  all  such  wheels  the  paddles  dip  into 
the  unconfined  current  which,  when  impeded  by  the  wheel,  heads 
up  and  passes  around  the  sides  of  the  wheel  and  thus  allows 
only  a  small  part  of  the  current  energy  to  be  utilized. 

3.  The  Undershot  Wheel. — The  introduction  of  a  channel  con- 
fining the  water  and  conducting  it  to  a  point  where  it  could  be 
applied  directly  to  the  undershot  wheel,  was  an  improvement  that 
permitted  the  utilization  of  about  thirty  per  cent,  of  the  theo- 


Fig.  2.— Float  Wheel  Operating  Pumps  for  Water  Supply  of  London  1581. 
(From  Matthews'  Hydraulia  Lond.  1835.) 


The  Overshot  and  Breast  Water  Wheel.  3 

retical  power  of  the  water.  This  form  of  water  wheel  was  most 
widely  used  for  power  development  until  the  latter  half  of  the 
eighteenth  century. 

In  the  float  and  undershot  wheels  the  energy  of  water  is  ex- 
erted through  the  impact  due  to  its  velocity.  The  heading  up 
of  the  water,  caused  by  the  interference  of  the  wheel,  results 
also  in  the  exertion  of  pressure  due  to  the  weight  of  the  water, 
but  this  action  has  only  a  minor  effect.  The  conditions  of  the 
application  of  the  energy  of  water  through  its  momentum  is  not 
favorable  to  the  high  efficiency  of  this  type  of  wheels  and  the 
determination  of  this  fact  by  Smeaton's  experiments  undoubt- 
edly was  an  important  factor  in  the  introduction  and  adoption  of 
the  overshot  water  wheel. 


Fig.  3.— Breast  Wheel  Used  From  About  1780  to  About  1870. 

4.  The  Overshot  and  Breast  Water  Wheel. — In  the  overshot 
water  wheel  the  energy  of  water  is  applied  directly  through  its 
weight  by  the  action  of  gravity,  to  which  application  the  design 
of  the  wheel  is  readily  adapted.  Such  wheels  when  well  con- 
structed have  given  efficiencies  practically  equal  to  the  best 
modern  turbine,  but  on  account  of  their  large  size  and  the  serious 
effects  of  back-water  and  ice  conditions,  they  are  unsatisfactory 
for  modern  power  plants  (see  Fig.  u). 

Following  the  work  of  Smeaton,  the  breast  wheel  (see  Fig.  3) 
was  developed  in  England  largely  through  the  work  of  Fairbairn 
and  Rennie.  The  latter  in  1784  erected  a  large  wheel  of  this 
type  to  which  he  applied  the  sliding  gate  from  which  the  water 
flowed  upon  the  wheel  instead  of  issuing  through  a  sluice  as 
formerly.  About  this  time  the  fly-ball  governor,  which  had  been 
designed  and  adapted  as  a  governor  for  steam  engines  by  Watt, 
was  applied  to  the  governing  of  these  wheels  and  by  means  of 
these  governors  the  speed  of  the  wheel  under  varying  loads  was 


Introduction. 


Fig.  4. — Breast  Wheel  About  1790  Showing  Early  Application  of  Governor. 

(After  Glynn.) 

kept  sufficiently  constant  for  the  purpose  to  which  they  were 
then  applied.     (See  Fig.  4.) 

Another  mode  of  applying  water  to  wheels  under  low  falls  was 
introduced  by  M.  Poncelet.  (See  Fig.  5.)  Various  changes  and 
improvements  in  the  form  of  buckets,  in  their  ventilation  so  as 
to  permit  of  complete  filling  and  prompt  emptying,  and  in  their 
structure,  took  place  from  time  to  time,  and  until  far  into  the 
middle  of  the  nineteenth  century  these  forms  of  wheels  were 
widely  used  for  water  power  purposes. 


Fig.  5.— Poncelet's  Wheel. 

5.  The  Development  of  the  Turbine. — The  invention  of  any 
important  machine  or  device  is  rarely  the  work  of  a  single  mind. 
In  general  such  inventions  are  the  result  of  years  of  experience 
of  many  men  which  may  be  simply  correlated  by  some  designer,. 


Fundamental  Idea  of  the  Turbine.  5 

to  whom  often  undue  credit  is  given.  To  the  man  who  has 
gathered  together  past  experiences  and  embodied  them  in  a  new 
and  useful  invention  and  perhaps  through  whose  energy  practical 
applications  are  made  of  such  inventions,  the  credit  is  frequently 
assigned  for  ideas  which  have  been  lying  dormant,  perhaps 
through  centuries  of  time.  Every  inventor  or  promotor  of  val- 
uable improvements  in  old  methods  and  old  construction  is  en- 
titled to  due  credit,  but  the  fact  should  nevertheless  be  recalled 
that  even  in  the  greatest  inventions  very  few  radical  changes  are 
embodied,  but  old  ideas  are  utilized  and  rearranged  and  a  new 
and  frequently  much  more  satisfactory  combination  results.  Im- 
provements in  old  ideas  are  the  improvements  which  are  the 
most  substantial.  Inventions  which  are  radically  new  and  strictly 
original  are  apt  to  be  faulty  and  of  little  practical  value. 


Fig.  6.— Ancient  Indian  Water  Wheel.     (After  Glynn.)     Containing  Fun- 
damental Suggestion  of  Both  Turbine  and  Impulse  Wheels. 

6.  Fundamental  Ideas  of  the  Turbine.— The  embryo  turbine 
may  be  distinguished  in  the  ancient  Indian  water  mill  (see  Fig.  6). 
A  similar  early  type  of  vertical  wheel  used  in  Europe  in  the  six- 
teenth century,  the  illustration  of  which  was  taken  from  aft  an- 
cient print  (see  Sci.  Am.  Sup.  Feb.  17,  '06)  is  shown  m  Fig.  7. 
Barker's  mill  in  its  original  form  or  in  the  form  improved  by 
M.  Mathon  de  Cour,  embodied  the  principal  idea  of  the  pressure 


6  Introduction. 

turbine,  and  was  used  to  a  considerable  extent  for  mill  purposes, 
In  1845  James  Whitlaw  suggested  an  improved  form  which  was 
used  in  both  England  and  Germany  early  in  the  nineteenth  cen- 
tury. (See  Fig.  8.)  Many  elements  of  the  modern  turbine  were 
conceived  by  Benjamin  Tyler,  who  received  letters  patent  for 
what  he  termed  the  "Wry  Fly"  wheel  in  1804.  The  description  of 
this  wheel  as  contained  in  the  patent  specifications  is  as  follows : 


Fig.  7. — Early  Vertical  Wheel.    Containing  fundamental  suggestion  of  the 

Turbine. 

'The  Wry  Fly  is  a  wheel  which,  built  upon  the  lower  end  of  a 
perpendicular  shaft  in  a  circular  form,  resembles  that  of  a  tub. 
It  is  made  fast  by  the  insertion  of  two  or  more  short  cones, 
which,  passing  through  the  shaft,  extend  to  the  outer  side  of  the 
wheel.  The  outside  of  the  wheel  is  made  of  plank,  jointed  and 
fitted  to  each  other,  dowreled  at  top  and  bottom,  and  hooped  by 
three  bands  of  iron,  so  as  to  make  it  water-tight;  the  top  must 
be  about  one-fifth  part  larger  than  the  bottom  in  order  to  drive 


Barker's  Mill. 


the  hoops,  but  this  proportion  may  be  varied,  or  even  reversed, 
according  to  the  situation  of  place,  proportion  of  the  wheel,  and 
quantity  of  water.  The  buckets  are  made  of  winding  timber,  and 
placed  inside  of  the  wheel,  made  fast  by  strong  wooden  pins 
drove  in  an  oblique  direction ;  they  are  fitted  to  the  inside  of  the 
tub  or  wheel,  in  such  a  manner  as  to  form  an  acute  angle  from 
the  wheel,  the  inner  edge  of  the  bucket  inclining  towards  the 
water,  which  is  poured  upon  the  top,  or  upper  end  of  it  about 
twelve  and  a  half  degrees ;  instead  of  their  standing  perpendicular 
with  the  shaft  of  the  wheel  they  are  placed  in  the  form  of  a 
screw,  the  lower  ends  inclining  towards  the  water,  and  against 
the  course  of  the  stream,  after  the  rate  of  forty-five  degrees ;  this, 
however,  may  be  likewise  varied,  according  to  the  circumstances 
of  the  place,  quantity  of  water,  and  size  of  the  wheel." 


Elevation. 


Plan  and  Partial  Section. 

Pig.  7.— Early  Vertical  Wheel.    Containing  Fundamental  Suggestion  of  the'T 

(After  Glynn.) 


Introduction, 


Fig.  9. — Roue  A'  Curves  (After  Glynn). 

From  the  description  it  will  be  noted  that,  with  the  exception 
of  the  chutes,  the  principal  features  of  the  modern  turbine  were 
here  anticipated.  The  "Wry  Fly"  wheel  was  an  improvement  on 
the  "tub"  wheel  which  was  then  in  use  to  a  considerable  extent 
in  the  country. 

These  various  early  efforts  received  their  first  practical  con- 
summation and  modern  solution  through  various  French  in- 
ventors early  in  the  nineteenth  century.  The  "Roue  a  dives'* 
(Fig.  9)  and  the  "Roue  Volant"  (Fig.  10)  had  long  been  used 
in  France,  and  were  the  subject  of  extensive  tests  by  MM.  Pio- 
bert  and  Tardy  at  Toulouse.  Those  various  wheels  received  the 
water  tangentially  through  an  opening  or  spout,  being  practically 
an  improvement  on  the  old  Indian  mill  by  the  addition  of  a  rim 
and  the  modification  of  the  form  of  buckets. 

7.  The  Modern  Turbine. — The  next  improvement  in  the  United 
States  consisted  in  the  addition  of  a  spiral  or  scroll  case  to  the 
wheel,  by  means  of  which  the  water  was  applied  equally  to  all 
parts  of  the  circumference  passing  inward  and  downward  through 
the  wheel.  To  the.  French  inventors,  Koechlin,  Fourneyron  and 
Jonval,  is  largely  due  the  design  of  the  turbine  in  a  more  modern 
and  practical  form.  By  the  middle  of  the  nineteenth  century 
these  wheels  had  met  with  wide  application  in  France  and  been 


The  Modern  Turbine, 


Fig.  10. — Roue  Volant  (After  Glynn). 

adopted  and  considerably  improved  by  American  and  German 
engineers,  but  were  scarcely  known  in  England.  (See  "Power 
of  Water,"  by  Jos.  Glynn,  1852.)  The  turbine  was  introduced 
into  the  United  States  about  1843  by  El  wood  Morris,  of  Penn- 
sylvania, but  was  developed  and  brought  to  public  attention  more 
largely  through  the  inventions  of  Uriah  A.  Boyden,  who  in  1844 
designed  a  seventy-five  horse-power  turbine  for  use  at  Lowell, 
Mass.  (See  Fig.  — ,  page  — .)  The  great  advantage  of  the  tur- 
bine over  the  old  style  water  wheel  may  be  summarized  as  fol- 
lowvS:  (See  Figs,  n  and  12.) 

I^irst :  Turbines  occupy  a  much  smaller  space. 

Second:  On  account  of  their  comparatively  high  speed  they 
can  frequently  be  used  for  power  purposes  without  gearing  and 
with  a  consequent  saving  in  power. 

Third :  They  will  work  submerged. 

Fourth :  They  may  be  utilized  under  any  head  or  fall  of  water. 
(Turbines  are  in  use  under  heads  as  low  as  sixteen  inches  and 
as  high  a?  several  hundred  feet.) 

Fifth :  Their  efficiency,  when  the  wheel  is  properly  constructed, 
is  comparatively  high. 

Sixth :  They  permit  a  greater  variation  in  velocity  without  ma- 
terial change  in  efficiency. 


IO 


Introduction. 


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Seventh :  They  are  more  readily  protected  from  ice  interfer- 
ence. 

8.  The  American  or  Francis  Turbine. — Through  the  efforts  of 
Uriah  A.  Boyden  and  James  B.  Francis  (1849),  the  Fourneyron 
turbine  became  the  leading  wheel  in  New  England  for  many 
years. 

In  1838  Samuel  B.  Howd  of  Geneva,  New  York,  patented  the 
'''inward  flow"  wheel,  in,  which  the  action  of  the  Fourneyron  tur- 
bine was  reversed.  This  seems  to  have  been  the  origin  of  the 
American  type  of  turbine,  and  the  Howd  wheel  was  followed  by 
a  large  number  of  variations  of  the  same  general  design  on 
which  American  practice  has  been  based  for  many  years.  About 
^849,  James  B.  Francis  designed  an  inward  flow  turbine  of  the 
same  general  type  as  the  Howd  wheel.  Two  of  these  wheels 


/c 


Fig.  13. — Inward  Flow  Wheel  by  S.  B.  Howd   (After  Francis). 

were  constructed  by  the  Lowell  Machine  Shop  for  the  Boott 
Cotton  Mills.  In  the  Lowell  hydraulic  experiments  (page  61) 
Mr.  Francis  refers  to  the  previous  patent  of  Howd  and  says: 
"Under  this  patent  a  large  number  of  wheels  have  been  con- 
structed and  a  great  many  of  them  are  now  running  in  different 


;i2  Introduction. 

parts  of  the  country.  They  are  known  in  some  places  as  the 
Howd  wheel,  in  others  as  the  United  States  wheel.  They  have 
uniformly  been  constructed  in  a  very  simple  and  cheap  manner 
in  order  to  meet  the  demands  of  the  numerous  classes  of  millers 
and  manufacturers  who  must  have  cheap  wheels  if  they  have 
any." 

Fig.  13  shows  a  plan  and  vertical  section  of  the  Howd  wheels 
as  constructed  by  the  owners  of  the  patent  rights  for  a  portion 
of  the  New  England  states.  In  this  cut  g  indicates  the  wooden 


Fig.   14.— Original  Francis  Turbine. 

•guides  by  which  the  water  is  directed  on  to  the  buckets ;  W  in- 
dicates the  wheel  which  is  composed  of  buckets  of  cast  iron 
fastened  to  the  upper  and  lower  crowns  of  the  wheel  by  bolts. 
The  upright  crown  is  connected  with  the  vertical  shaft  S  by  arms. 
The  regulating  gate  is  placed  outside  of  the  guides  and  is  made 
-of  wood.  The  upright  shaft  S  runs  on  a  step  at  the  bottom  (not 
shown  in  the  cut).  The  projections  on  one  side  of  the  buckets, 
it  was  claimed,  increased  the  efficiency  of  the  wheel  by  diminish- 
ing the  waste  of  the  water. 

The  wheel  designed  by  Francis  was  on  more  scientific  lines,  of 
better  mechanical  construction  (see  Fig.  14)  and  is  regarded  by 


Modern  Changes  in  Turbine  Practice.  13 

many  as  the  origin  of  the  American  turbine.  The  credit  of  this 
design  is  freely  awarded  to  Francis  by  German  engineers,  this 
type  of  wheel  being  known  in  Germany  as  the  Francis  Turbine. 
The  Francis  wheel  was  followed  by  other  inward  flow  wheels  of 
a  more  or  less  similar  type.  The  Swain  wheel  was  designed  by 
A.  M.  Swain  in  1855.  The  American  turbine  of  Stout,  Mills  and 
Temple  (1859),  the  Leffel  wheel,  designed  by  James  Leffel  in 
1860,  and  the  Hercules  wheel,  designed  by  John  B.  McCormick 
in  1876,  are  among  the  best  known  and  earliest  of  the  wheels  of 
this  class. 

g.  Modern  Changes  in  Turbine  Practice. — A  radical  change  has 
taken  place  in  later  years  in  the  design  of  turbines  by  the  adop- 
tion of  deeper,  wider  and  fewer  buckets  which  has  resulted  in  a 
great  increase  of  power  as  shown  by  the  following  table  from  a 
paper  by  Samuel  Webber  (Transactions  of  Am.  Soc.  M.  E. 
Vol.  XVII)  : 


TABLE  I.— Showing  Size,  Capacity  and  Power  of  Various  Turbines  Under 

a  26-foot  Head. 


Inches 
Diameter. 

Cubic  Feet 
'  Water  per 
Second. 

Horse 
Power. 

Boyden-Fourneyron  

36 

22.95 

55 

Ripdon  

36 

35.45 

89 

Risdon  "L  C."  

36 

48.27 

121 

Risdon  "L   1)  "  

36 

80. 

199 

Leffel,  Standard  

36 

40.45 

96 

Leffel,  Special  

35 

60. 

148 

Tyler  

36 

40.7 

95.8 

Swain  

36 

58.2 

140 

Hunt    "Swain  bucket"                      

36 

48.8 

121 

Hunt  New  Style                          

36 

98. 

239.74 

Leffel    "Samson"                             

3,5 

109.1 

264 

"Hercules"                        

36 

107.6 

253.5 

"Victor"                            

25 

108.8 

266 

New  Swain          

36 

89.5 

215 

By  1870  the  turbine  had  largely  superseded  the  water  wheel 
for  manufacturing  purposes  at  the  principal  water  power  plants 
in  this  country.  The  old  time  water  wheel  has  since  become  of 
comparatively  small  importance,  but  it  is  still  used  in  many  iso- 
lated places  where  it  is  constructed  by  local  talent,  and  adapted 
to  local  conditions  and  necessities. 


14  Introduction. 

The  current  wheel  is  still  widely  used  for  irrigation  purposes 
and  in  many  instances  is  a  useful  and  valuable  machine. 

10.  Historical  Notes  on  Water  Power  Development. — Water 
mills  were  introduced  at  Rome  about  seventy  years  B.  C.   (see 
Strabo  Lib.  XII),  and  were  first  erected  on  the  Tiber.    Vitruvius 
describes  their  construction  as  similar  in  principle  to  the  Egyp- 
tian Tympanum.     To  their  circumference  were  fixed  floats  or 
paddles  which  when  acted  upon  by  the  current  of  the  stream 
drove  the  wheel  around.    Attached  to  this  axis  was  another  ver- 
tical wheel  provided  with  cogs  or  teeth.  A  large  horizontal  wheel 
toothed  to  correspond  with  it  worked  on  an  axis,  the  upper  head 
of  which  was  attached  to  the  mill  stone.    The  use  of  such  water 
wheels  became  very  common  in  Italy  and  in  other  countries  sub- 
ject to  Roman  rule. 

Some  of  the  early  applications  of  water  power  are  of  interest. 
In  1581  a  pump  operated  by  a  float  wheel  was  established  at 
London  Bridge  to  supply  the  city  of  London  with  water.  In 
1675  an  elaborate  pumping  plant  driven  by  water  wheels  was 
established  on  the  Seine  river  near  Saint  Germain.  For  this 
plant  a  dam  was  constructed  across  the  river  and  chutes  were 
arranged  to  conduct  the  water  to  the  undershot  water  wheels. 
These  were  twelve  or  more  in  number,  each  operating  a  pump 
that  raised  the  waters  of  the  Seine  into  certain  reservoirs  and 
aqueducts  for  distribution. 

The  pumping  of  water  for  agricultural  irrigation  and  drainage, 
domestic  supplies  and  mine  drainage,  was  undoubtedly  the  first 
application  of  water  power,  and  still  constitutes  an  important 
application  of  water.  Fig.  15,  from  an  article  by  W.  F.  Dupfee, 
published  in  Cassier's  Magazine  of  March,  1899,  illustrates  a 
primitive  application  of  the  water  wheel  to  the  pumping  of  water 
from  mines.  The  frontispiece  also  shows  the  great  Laxy  over- 
shot water  wheel  in  the  Isle  of  Man  which  is  still  used  for  mine 
drainage.  The  wheel  is  about  seventy  feet  in  diameter  and  the 
water  is  brought  from  the  hills  a  considerable  distance  for  power 
purposes. 

11.  Development  of  Water  Power  in  the  United  States. — In 
this  country  one  of  the  first  applications  of  water  power  was  the 
old  tidal  mill  on  Mill  Creek  near  Boston,  constructed  in  1631, 
which   was   followed   by  the   extensive   developments   of   small 
powers  wherever  settlements  were  made  and  water  power  was 


Development  of  Water  Power. 


available.      Often   availability   of   water   power   determined   the 
location  of  the  early  settlement. 

About   1725  the  first  power  plant  was  established  along  the 
Niagara  River.     This  was  a  water-driven  saw-mill  constructed 

Chronological  Development  of  Water  Power  of  the  United  States  to  1898. 


Year. 

Fall 
Ft. 

Minimum 
Horse 
Power. 

Drainage 
Area  Sq. 
Miles. 

Lowell    Mass       

1822 

35 

1  1  ,  845 

4  083 

Nashua,   N   H  

1823 

36 

1,200 

516 

Oohoes,  N.  Y  

1826 

104 

9,450 

3,490 

Norwich,  Conn  

1828 

16 

700 

1,240 

Augusta.  Me 

1834 

17 

3,5(JO 

5  907 

Manchester  N    H 

1835 

52 

12,000 

2,  839 

Hooksett    N  H 

184L 

14 

1,8(0 

2,791 

Lawrence  Mass 

1845 

30 

11,000 

4,625 

A  uo'usta  Ga  

1847 

50 

8,500 

8,830 

Holyoke,  Mass  ....         

1848 

50 

14,000 

8,000 

Lewiston,  Me  

1849 

50 

11,900 

3,200 

Columbus,  Ga  

1850 

25 

10,000 

14,900 

Rochester,  N.  Y  . 

1856 

236 

8,000 

2,474 

St.  Anthony  Falls,  Minn  

1857 

50 

15,500 

19,736 

Niagara,  N.  Y.  (Hy.  canal)  
Turner's  Falls   Conn 

1861 
1866 

90 
35 

15,000 
10,000 

271,000 
6,000 

Fox  River  Wis 

1866 

185 

6,449 

Birmingham    Conn 

1870 

22 

1,000 

2,000 

Bangor,  Me  ... 

1876 

9 

1,767 

7,200 

Augusta,  Ga.  .  .     .           

1876 

50 

8,500 

6,830 

Palmer's  Falls,  N  Y  

1882 

30 

1,125 

2,650 

Mechanicsville,  N   Y  

1882 

20 

3,  636 

4,476 

St.  Cloud,  Minn  

1885 

14 

4,500 

13,250 

Little  Falls,  Minn  

1887 

14 

4,000 

11,084 

Spokane  \Vash 

1888 

70 

18,000 

4,180 

Howland   Me 

1888 

22 

6,000 

Great  Falls,  Mont  

1890 

42 

16,000 

22,000 

Austin  Texas                              

1891 

ne 

10,000 

40,  000 

Sault  Ste  Marie   Out     .           

1891 

18 

10,  000 

51,600 

In'olsom    Cal 

1891 

55 

6,200 

Concord,  N   H  

1894 

13 

5,000 

2,350 

Niagara,  N.  Y.  (tunnel)  
O^den   Utah 

1894 
1896 

170 
446 

50,  000 
2,  U40 

271,000 
3«0 

Helena  Mont 

'    1897 

32 

10,000 

14,900 

Minneapolis    Minn                         ... 

1897 

18 

6,000 

19,737 

Mechanicsville  NY          

1898 

18 

3,270 

4,478 

by  the  French  to  furnish  lumber  for  Fort  Niagara.  Mr.  J.  T. 
Fanning  gives  the  following  list  of  the  dates  of  establishing  some 
of  the  principal  water  powers  of  the  United  States : 

The  last  few  years  have  witnessed  a  still  more  rapid  develop- 
ment.    The  increase  in  manufacturing  industries  and  other  de- 


i6 


Introduction 


mands  for  power  and  energy,  the  increased  cost  of  coal,  and  the 
improvement  in  electrical  methods  of  generation  and  transmis- 
sion have  all  united  to  accelerate  the  development  of  water  power 
plants.  Water  powers  once  valueless  on  account  of  their  dis- 
tance from  centers  of  manufacturing  and  population  are  now 
accessible  and  such  powers  are  rapidly  being  developed  and  their 
energy  brought  into  the  market. 


Fig.  15.— Early  Application  of  Undershot  Water  Wheel  to  Mine  Drainage, 
Date  Unknown  (from  Cassiers  Mag.  March,  1899). 


LITERATURE. 

1.  Appleton's  Cyclopedia  of  Applied   Mechanics.     Modern   Mechanis'm,   Vol. 

3,  pp.  891-901.     Description  of  the  development  of  the  turbine. 

2.  Spon's   Dictionary  of  Engineering.     Barker's   Mill,   pp.    230-235. 

do.     Float  Water  Wheels  (including  undershot  wheels),  pp.  1511-1524. 

do.     Overshot  Water  Wheels,  p.  2557. 

do.     Poncelet's  Water  Wheels,  p.  26GO. 

do.     Turbine  Water  Wheels,  pp.  3014-3022. 

3.  Knight's  Mechanical  Dictionary,  Vol.   3,   Water     Wheels,   p.   2746;    Tur 

bines,  pp.  2G5G-2G58. 


Literature.  17 

4.  Emerson,   James.     Hydrodynamics.     Published  by  author.     Willimansett, 

Mass.  1892.     Describes  several  types  of  American  turbines. 

5.  Matthews,  William.     Hydraulia.     London,  1835.     (Description  of  London 

Bridge  Water  Wheels,  p.  28.) 

6.  Fairbairn,  William.     Machinery  and  Millwork.     Description  of  undershot 

water  wheel,  pp.  145-150;  description  of  earlier  types  of  tur- 
bines, pp.  151-173. 

7.  Francis,  James  B.     Lowell  Hydraulic  Experiments,     pp.   1-70.     Descrip- 

tion and  tests  of  Boyden-Fourneyron  Tremond  Turbines;  also 
the  Boyden-Francis  "Center-Vent"  Turbine,  in  which  the  Flow 
was  Radially  Inward.  New  York,  D.  Van  Nostrand,  1883. 

8.  Weisbach,    P.    J.     Mechanics    of    Engineering,    vol.    II.     Hydraulics    and 

Hydraulic  Motors1.  Translated  by  A.  J.  DuBois.  New  York, 
J.  Wiley  &  Sons. 

9.  Morin,  Arthur.     Experiments  on  Water  Wheels  having  a  Vertical  Axis, 

Called  Turbines,  1838.  Translated  by  Ellwood  Morris  in  Jour. 
Franklin  Inst,  3d  ser.,  vol.  6,  1843,  pp.  234-246,  289-302,  370-377. 
370-377. 

10.  Morris,    Ellwood.     Remarks    on    Reaction    Water    Wheels    Used    in    the 

United  States  and  on  the  Turbine  of  M.  Fourneyron.  Jour. 
Franklin  Inst,  3d  ser.,  Vol.  4,  1842,  pp.  219-227,  289-304. 

11.  Morris,  Ellwood.     Experiments  on  the  Useful  Effect  of  Turbines  in  the 

United  States.  Jour.  Franklin  Inst,  3d  ser.,  Vol.  6,  1843, 
pp.  377-384. 

12.  Whitelaw,    James.     Observations   of    Mr.    Ellwood    Morris's    Remarks   on 

Water  Wheels.  Jour.  Franklin  Inst,  3d  ser.,  Vol.  8,  1844, 
pp.  73-80. 

13.  Franklin    Institute.     The    Koechlin    Turbine.     Jour.    Franklin    Inst,    3d 

ser.,  Vol.  20,  1850,  pp.  189-191.  (Report  of  experiments  made 
by  members  of  the  institute  at  the  request  of  Emile  Geyelin, 
who  introduced  the  Koechlin  turbine  at  Dupont's  powder  mill.) 

14.  Ewbank,  Thos1.     Hydraulic  and  Other  Machines  for  Raising  Water.     New 

York,  1847. 

15.  Geyelin,   Emile.     Experiments   on   Two   Hydraulic   Motors,    Showing  the 

Comparative  Power  Between  an  Overshot  Wheel  and  a  Jonval 
Turbine  made  for  Troy,  N.  Y.  Jour.  Franklin  Inst.,  3d  ser., 
Vol.  22,  1851,  pp.  418,  419. 

16.  Glynn,   Joseph.     Power  of  Water.     London,   1850.     pp.    39-97.      Weales 

Scientific  Series. 

17.  Webber,  Samuel.   Ancient  and  Modern  Water  Wheels.   Eng.  Mag.,  Vol.  1, 

1891,  pp.  324-331. 

18.  Frizell,  J.  P.     The  Old-Time  Water  Wheels  of  America.    Trans.  Am.  Soc. 

C.  E.,  Vol.  28,  1893,  pp.  237-249. 

19.  Aldrich,  H.  L.     Water  Wheels.     Description  of  Various  Types  of  Ameri- 

can Wheels.    Power,  Vol.  19,  No.  11,  1894. 

20.  Francis,   James.     Water   Power    in   New   England.      Eng.    Rec.,   Vol.    33, 

1896,  pp.  418,  419. 
2 


iS  Introduction. 

21.  Geyelin,  Emile.     First  Pair  of  Horizontal  Turbines  ever  Built  Working 

on   a   Common   Axis.      Proc.    Eng.    Club,   Philadelphia,   Vol.   12, 

1895,  pp.   213,  214. 

22.  Francis,   James.     Water   Power   in   New    England.      Eng.    Rec.    Vol.    33, 

1896,  pp.  418,  419. 

23.  Webber,  Samuel.   Water  Power,  its  Generation  and  Transmission.    Trans. 

Am.  Soc.  Mech.  Eng.,  Vol.  17,  189G,  pp.  41-57. 

24.  Tyler,  W.  W.     The  Evolution  of  the  American  Type  of  Water  Wheel. 

Jour.  West.  Soc.  Eng.,  Chicago,  Vol.  3,  1898,  pp.  879-901. 

25.  Johnson,  W.  C.     Power  Development  at  Niagara.     Jour.  Asso.  Eng.  Soc., 

July,  1899,  pp.  78-90.  Hist,  of  early  development  of  power  at 
Niagara. 

26.  Christie  W.  W.     Some  Old-Time  Water  Wheels.     Description  of  Various 

old  wheels  in  Eastern  U.  S.  Eng.  News,  Vol.  42,  1899,  pp. 
394-395. 

27.  Ruchel,  E.     Turbines  at  the  World's  Fair,  Paris,  1900.     Review  of  Tur- 

bine development  in  various  countries.  Zeitschr.  d  ver  Deutsch, 
Ing.  p.  657,  1900. 

28.  Foster,  H.  A.    The  Water  Power  at  Holyoke.    Jour.  Asso.  Eng.  Soc.,  Vol. 

25,  1900,  pp.  67-84. 

29.  Thomas,    R.     Development   of   Turbine    Construction.      Zeitschr.    d    ver 

Deutsch.  Ing.  p.  409,  1901. 

30.  Rice,  A.  C.     Notes  on  the  History  of  Turbine  Development  in  America. 

Eng.  News,  Vol.  48,  1902,  pp.  208-209. 

31.  Fanning,  J.  T.    History  of  the  Development  of  American  Water  Powers. 

Rept.  22d  Ann.  Meeting,  Am.  Paper  and  Pulp  Asso.,  1898,  pp. 
16-24.  Progress1  in  Hydraulic  Power  Development.  Eng.  Rec- 
ord, Vol.  47,  1903,  pp.  24-25. 

32.  Fanning,  J.  T.     Progress  in  Hydraulic  Power  Development.     Eng.  Rec- 

ord, Jan.  3d,  1903. 

33.  Sickman,  A.  F.     The  Water  Power  at  Holyoke.    Jour.  N.  E.  W.  W.  Asso., 

Vol.  18,  1904,  pp.  337-351.     Historical. 


CHAPTER    II. 

POWER. 

12.  The  Development  of  Potential  Energy. — The  development 
of  natural  sources  of  potential  energy,  the  transformation  of  such 
energy  into  forms  which  can  be  utilized  for  power,  and  its  trans- 
mission to  points  where  it  can  be  utilized  for  commercial  pur- 
poses, constitutes  a  large  portion  of  the  work  of  the  engineer. 
The  water  power  engineer  primarily  deals  with  energy  in  the 
form  of  flowing  or  falling  water,  but  his  knowledge  must  extend 
much  further  for  he  encounters  other  forms  of  energy  at  every 
turn.     Much  of  the  energy  available  from  the  potential  source 
will  be  lost  by  friction  in  bringing  the  water  to  and  taking  it 
from  the  wheel.     Much  is  lost  in  hydraulic  and  mechanical  fric- 
tion in  the  wheel ;  additional  losses  are  sustained  in  every  trans- 
formation,  and,   if  electric  or  other  forms  -of  transmission  are 
used  or  auxiliary  power  is  necessary  for  maintaining  continuous 
operation,  the  engineer  will  be  brought  in  contact  with  energy 
in  many  other  forms. 

13.  Definition  of  Energy. — Energy  is  the  active  principle  of 
nature.     It  is  the  basis  of  all  life,  all  action,  and  all  physical 
phenomena.     It  is  the  ability  to  exert  force,  to  overcome  resist- 
ance, to  do  work.    All  physical  and  chemical  phenomena  are  but 
manifestations  of  energy  transformations,  and  all  nature  would 
be  rendered  inactive  and  inanimate  without  these  changes. 

14.  Solar  Energy  the  Ultimate  Source. — A  brief  consideration 
of  the  various  sources  of  potential  energy  makes  the  fact  mani- 
fest that  solar  energy  is  the  ultimate  source  from  which  all  other 
forms  are  directly  or  indirectly  derived.    The  variations  in  solar 
heat  on  the  earth's  surface  produces  atmospheric  currents  often 
of  tremendous  power.     This  form  of  energy  may  be  utilized,  in 
its  more  moderate  form,  to  drive  the  sailing  vessel  and  the  wind- 
mill, and  in  other  ways  to  be  of  service  to  man.    The  energy  of 
fuel  is  directly  traceable  to  solar  action.     Through  present  and 
past  ages  it  has  been  the  active  cause  of  chemical  and  organic 


2O  Power 

change  and  growth.  From  this  has  resulted  fuel  supplies  avail- 
able in  the  original  form  of  wood,  or  in  the  altered  forms,  from 
ancient  vegetation  to  the  forms  of  coal,  oil  and  gas,  and  from 
which  a  large  portion  of  the  energy  utilized  commercially  is 
derived. 

A  brief  study  of  meteorological  conditions  shows  that  through 
the  agency  of  solar  heat,  and  the  resulting  atmospheric  move- 
ment, a  constant  circulation  of  water  is  produced  on  and  near 
the  earth's  surface.  Hundreds  of  tons  of  water  are  daily  evapor- 
ated from  the  seas,  lakes,  rivers  and  moist  land  surface,  rise  as 
vapor  into  the  atmosphere,  circulate  with  the  winds,  and,  under 
favorable  conditions,  are  dropped  again  upon  the  earth's  surface 
in  the  rainfall.  Those  portions  of  the  rain  that  fall  upon  the 
land  tend  to  flow  toward  the  lower  places  in  the  earth's  crust, 
where  lie  the  seas  and  oceans,  and  such  portions  of  these  waters 
as  are  not  absorbed  by  the  strata,  evaporated  from  the  surface 
or  utilized  in  plant  growth,  ultimately  find  their  way  to  these 
bodies  of  water  to  again  pass  through  this  cycle  of  changes  which 
is'  constantly  in  progress.  Thus  we  find  water  always  in  motion, 
and  always  an  active  agent  in  nature's  processes.  Due  to  its 
peculiar  physical  properties  and  chemical  relations,  it  is  one  of 
the  essential  requisites  of  life,  and  is  also  of  great  importance  in 
nature's  processes  through  the  energy  of  which  it  is  the  vehicle. 

15.  No  Waste  of  Energy  in  Nature. — Active  continuous  en- 
ergy transformation  is  a  most  important  natural  phenomenon. 
Changes  from  one  form  to  another  are  constantly  in  progress. 
In  nature's  transformations  energy  is  always  fully  utilized.  As 
the  running  stream  plunges  over  the  fall,  the  potential  energy, 
due  to  its  superior  elevation,  is  transformed  into  the  kinetic  en- 
ergy of  matter  in  motion,  and  through  the  shock  or  impact  the 
kinetic  energy  is  transformed  into  thermal  energy  due  to  a  higher 
temperature,  which  again  may  be  partially  changed  in  form  by 
radiation  or  vaporization.  Thus  the  quantity  of  energy  is  con- 
tinually maintained,  while  its  quality  or  conditions  constantly 
vary.  There  is,  and  can  be,  no  waste  or  loss  of  energy  as  far  as 
nature  itself  is  concerned.  Wasted  or  lost  energy  are  terms  that 
apply  only  to  energy  as  utilized  in  the  service  of  man.  Nature 
itself  never  seems  to  utilize  the  entire  quantity  of  energy  from 
one  source  for  the  development  of  energy  of  a  single  form,  but 
always  differentiates  from  one  form  into  a  number  of  other  forms. 
When  the  engineer  therefore  attempts  to  utilize  any  source  of 


Laws  of  Energy  Conservation.  21 

potential  energy  for  a  single  purpose,  he  at  once  encounters  this 
natural  law  of  differentiation  and  finds  it  impossible  to  utilize 
more  than  a  portion  of  the  energy  used  in  the  manner  in  which 
he  desires  to  utilize  it.  Much  of  this  loss  may  be  due  to  the  form 
of  energy  available,  much  to  the  medium  of  transformation  and 
transmission,  and  much  to  physical  difficulties  which  it  is  im- 
possible to  overcome. 

1 6.  Laws  of  Energy   Conservation. — Primarily   it   should   be 
fully  understood  and  clearly  appreciated  that  matter  and  energy 
can  neither  be  created  nor  destroyed.     Both  may  be  changed  in 
form  or  they  may  be  dissipated  or  lost  so  far  as  their  utilization 
for  commercial  needs  is  concerned.     But  in  one  form  or  another 
they  exist,  and  their  total  amount  in  universal  existence  is  al- 
ways the  same.     In  any  development  for  the  utilization,  trans- 
formation or  transmission  of  energy,  the  following  fundamental 
axioms  must  be  thoroughly  understood  and  appreciated: 

First :  That  the  amount  of  energy  which  can  be  actually  utilized 
in  any  machine  or  system  can  never  be  greater  than  the  amount 
available  from  the  potential  source. 

Second:  That  the  amount  of  energy  which  can  be  utilized  in 
any  such  system  can  never  be  greater  than  the  difference  be- 
tween the  amount  entering  the  system  and  the  amount  passing 
from  the  system  as  waste  in  the  working  medium. 

17.  Efficiency. — Efficiency  is  the  ratio  or  percentage  of  energy 
utilized  to  energy  applied  in  any  system,  part  of  a  system,  ma- 
chine or  in  any  combination  of  machines. 

The  efficiency  of  a  given  machine  or  mechanism,  or  the  per- 
centage of  available  energy  which  can  be  obtained  from  a  given 
system  of  generation  and  transmission  therefore  can  never  be 
greater  than  represented  by  the  equation : 

•pi -pi  i 

Efficiency  or  amount  of  available  energy  = = —  in  which 

jii 

E  equals  the  energy  in  the  working  medium  entering  the  machine 

E'  equals  the  energy  in  the  working  medium  passing  from  the  machine. 

1 8.  Natural  limit  to  efficiency. — The  total  energy  in  a  working 
medium  such  as  water,  steam,  air,  etc.,  is  the  energy  measured 
from  the  basis  of  the  absolute  zero  for  the  medium  which  is 
being  considered.     For  example,  the  average  surface  of  Lake 
Michigan  is  580  feet  above  sea  level ;  each  pound  of  water,  there- 
fore, at  lake  level  contains  580  foot  pounds  of  potential  energy. 
This  amount  of  energy  must  therefore  be  expended  in  some  man- 


22  .       Power. 

ner  by  each  pound  of  water  passing  from  the  lake  level  to  the 
ocean  level,  which  may  be  regarded  as  the  absolute  zero  refer- 
ence plane  for  water  power.  This  energy  cannot  be  utilized  at 
Chicago  for  there  no  fall  is  available.  A  small  portion  of  this 
energy  is  now  utilized  in  the  power  plants  at  the  falls  of  Niagara. 
Some  energy  will  be  ultimately  utilized  on  the  Chicago  Drainage 
Canal,  where  a  fall  of  some  thirty-four  feet  is  available  from  the 
controlling  works  to  Joliet.  Perhaps  ultimately  in  its  entire 
course  one  hundred  and  seventy  feet  of  fall  may  be  utilized  by 
the  waters  of  the  drainage  canal,  in  which  case  the  absolute  avail- 
able energy  of  each  pound  of  water  cannot  be  greater  than  shown 
by  the  following  equation : 

Available  energy  = ^^ —    =  — —  =  .2931,  or  29.31  per  cent. 

OoU  OoU 

With  any  other  form  of  energy  the  same  conditions  also  pre- 
vail. Consider  a  pound  of  air  at  760  degrees  absolute  tempera- 
ture Fahr.,  and  at  75  pounds  absolute  pressure.  The  number  of 
heat  units  contained  will  be  given  by  the  equation : 

Heat  units  —  temperature  X  weight  X  specific  heat. 
B.  T.  U.  =  760  degrees  X  1  X  .169  =  128. 

To  utilize  all  of  the  energy  in  this  air,  it  would  be  necessary 
to  expand  it  down  to  a  temperature  of  absolute  zero  and  exhaust 
it  against  zero  pressure.  In  any  machine  for  utilizing  com- 
pressed air,  it  will  be  necessary  to  exhaust  it  against  atmospheric 
pressure.  This  will  expand  the  air  3.10  times,  and  if  expanded 
adiabatically  it  will  have  a  final  temperature  of  474  degrees.  The 
heat  units  in  the  exhaust  will  therefore  be  as  follows : 

B.  T.  U.  =  474  degrees  X  1  X  .169  =  80, 
and  the  available  energy  will  be  as  follows : 

1  OO     QA  AQ 

Available  energy  =  ±^—     -  =  -^-  =  .375,  or  37.5  per  cent. 

IZo  iZo 

In  this  case  also  the  temperatures  vary  directly  as  the  heat 
units,  and  are  therefore  a  measure  of  available  energy: 

«  ygQ 474 

Available  energy  = — —  =  .375  or  37.5  per  cent. 

In  the  ideally  perfect  furnace  the  efficiency  is  somewhat  higher. 
The  fuel  may  be  consumed  at  a  temperature  of  about  4,000  Fahr. 
absolute,  and  the  gas  may  be  cooled  before  escaping  to  about  600 
Fahr.  In  this  case  the  possible  efficiency  or  available  energy  is : 


Practical  Limits  to  Efficiency.  23 


4QOO  _  QQQ 

Available  energy  =  --    --  -  =  .832  or  83.2  per  cent. 


The  above  examples  show,  therefore,  the  limits  which  nature 
itself  places  on  the  proportion  of  energy  which  it  is  theoretically 
possible  to  utilize.  For  such  losses  the  engineer  is  not  account- 
able except  for  the  selection  of  the  best  methods  for  utilizing 
such  energy.  The  problem  for  his  solution  is,  what  amount  of 
this  available  energy  can  be  utilized  by  efficient  machines  and 
scientific  methods. 

19.  Practical  Limits  to  Efficiency.  —  The  preceding  equations 
are  the  equations  of  ideally  perfect  machines.  Of  this  available 
energy  only  a  portion  can  be  made  actually  available.  In  practice 
we  are  met  with  losses  at  every  turn.  Some  energy  will  be  lost 
in  friction,  as  radiated  heat,  some  in  the  slip  by  pistons,  or  as 
leakage  from  defective  joints.  In  many  other  ways  the  energy 
applied  may  be  dissipated  and  lost.  From  this  it  follows  : 

The  amount  of  energy  'which  can  be  utilized  can  never  be 
greater  than  the  difference  between  the  amount  supplied  to  any 
given  machine  or  mechanism,  and  the  amount  lost  or  consumed 
in  such  machines  by  friction,  radiation  or  in  other  ways.  Hence 
it  follows  that  the  efficiency  of  a  given  machine,  or  the  percent- 
age of  energy  available,  or  which  can  be  obtained  from  the  ma- 
chine, can  never  be  greater  than  the  following: 

E  —  CE;  +E"  +  E"'  +E""etc.)  .• 
Efficiency  —  -        -  —  -  ^  --  !  -  -  in  which 

E  =  total  energy  available 

E'  E"  E"'  etc.  —  the  energy  lost  in  friction  and  in  various  other  ways,  in 
the  machine  or  system,  and  rejected  in  the  exhaust  from  the  same. 

Every  transmission  or  transformation  of  energy  entails  a  loss, 
hence,  starting  with  a  given  quantity  of  energy,  it  gradually  dis- 
appears by  the  various  losses  involved  in  the  mechanism  or  ma- 
chines used.  Other  things  being  equal,  the  simpler  the  trans- 
mission or  transformation,  the  greater  the  quantity  of  the  orig- 
inal amount  of  energy  that  can  be  utilized. 

The  term  efficiency  as  here  applied  represents  always  the  ratio 
between  the  energy  obtainable  from  the  mechanism  or  machine 
and  the  actual  energy  applied  to  it. 

Therefore  the  efficiency  of  a  pumping  engine  is  the  ratio  be- 
tween the  energy  of  the  water  leaving  the  pump  and  the  energy 
of  the  steam  applied  to  the  engine. 


24 


Power. 


The  efficiency  of  a  hydro-electric  plant  is  the  ratio  between  the 
energy  in  the  electric  current  delivered  at  the  switch  board  and 
the  energy  in  the  water  entering  the  water  wheel. 

The  efficiency  of  the  dynamo  in  the  same  plant  is  the  ratio  be- 
tween the  energy  furnished  by  the  dynamo  and  the  energy  ap- 
plied to  it. 

If  a  shaft  receives  from  an  engine  100  horse  power  and  de- 
livers 90,  ten  horse  power  being  lost  in  friction,  etc.,  the  efficiency 
of  the  shaft  transmission  is  90  per  cent. 

If  a  steam  engine  receives  1,000,000  heat  units  from  the  steam 
it  uses,  and  is  able  to  deliver  only  the  equivalent  of  10,000  heat 
units ;  i.  e.,  7,780,000  foot  pounds  of  work,  the  efficiency  of  the 
engine  is  only  one  per  cent. 

20.  Efficiency  of  a  Combined  Plant. — In  any  plant  or  connected 
arrangement  of  mechanisms  and  machines  for  the  transforma- 
tion or  transmission  of  energy  the  efficiency  of  the  plant  is  the' 
product  of  the  efficiency  of  each  of  its.  parts. 

Hence,  to  estimate  total  efficiencies,  the  efficiency  of  each  part 
may  be  estimated,  and  the  combined  efficiency  then  obtained. 
From  the. same  calculation,  the  necessary  relations  between  the 
input  and  the  output  of  energy  can  be  obtained.  Thus,  if  a 
boiler  has  an  efficiency  of  50  per  cent.,  and  an  engine  has  an 
efficiency  of  10  per  cent,  the  combined  efficiency  will  be  .5oX.io 
=.05  or  five  per  cent. 

In  the  following  examples  the  loss  and  efficiency  of  the  unit 
and  the  combined  efficiency  of  the  various  units  in  the  system 
are  shown. 

FIRST  EXAMPLE. 
Example  of  Energy  Loss  in  Well-Designed  Steam  Power  Plant. 


Per  Cent 

Lost. 

Per  Cent 
Efficiency 

Net  Effi- 
ciency from 
Potential 
Source. 

20 

80 

80 

Boiler           .       . 

15 

85 

68 

Steam  Pipe  

5 

,95 

64.5 

Engine    

94 

6 

3.87 

Belt  

5 

95 

3  .  67 

Shafting,  Belts  and  Counter  Shafts  

40 

60 

2.2 

Lathes  or  other  Machine  Tools 

50 

50 

1.1 

Percentage  of  original  energy  utilized  in 
useful  work  

1  1 

Efficiency  of  a  Combined  Plant.  25 

SECOND  EXAMPLE. 
Example  of  Energy  Loss  in  Hydraulic  Plant  for  Electric  Lighting. 


Per  Cent 
Lost. 

Per  Cent 
Efficiency 

.Net  Effi- 
ciency from 
Potential 
Source. 

Head  and  Tail  Races  

5 

95 

95 

Turbine  

20 

80 

76 

Gearing  

15 

85 

64  6 

Shaft  

5 

95 

60  37 

Belt  

5 

95 

57  35 

8 

92 

52  76 

10 

90 

47  48 

Transformer  

20 

80 

37  98 

Lamp  

80 

20 

7  60 

Percentage  of  original  energy  utilized  in 
useful  work  

7  60 

THIRD  EXAMPLE. 
Example  of  Energy  Lost  in  Steam  and  Electric  Pumping  Plant. 


Per  Cent 
Lost. 

Per  Cent 
Efficiency 

Net  Effi- 
ciency from 
Potential 
Source. 

30 

70 

70 

Steam  Pipe  

5 

95 

66.6 

90 

10 

6.65 

Belt  

5 

95 

6.32 

Generator  

20 

80 

5.05 

Line  

10 

90 

4.55 

Motor                                                           

10 

90 

4'.  09 

25 

75 

3.06 

Suction  and  Discharge  Pipe       

20 

80 

2.45 

Percentage  of  original  energy   utilized  in 

2.45 

21.  Capacity  of  Each  Part  of  a  System  Not  Identical. — In  each 
of  .  the  transmission  systems  outlined  above  a  much  larger 
amount  of  energy  enters  the  first  unit  of  the  system  than  is  de- 
livered by  the  last.  Each  unit  in  the  system  receives  a  decreas- 
ing amount  of  energy. 

In  consequence,  the  first  units  in  the  system  must  be  of  greater 
proportional  capacity,  and  in  practice  each  unit  must  be  selected 
of  a  size  or  capacity  suited  for  its  position  in  the  system.  Thus 
in  the  first  example,  for  each  100  units  of  energy  received  by  the 
furnace,  the  engine  receives  but  64.5,  and  the  shafting  but  4. 


26  Power. 

22.  The  Analysis  of  Losses. — In  estimating  power  losses  the 
loss  in  each  step  from  the  generation  to  the  utilization  of  the 
power  should  be  carefully  examined.     Four  steps  may  ordinarily 
be  considered  in  any  system : 

1.  Generation  of  power  from  potential  source. 

2.  Conversion  of  power  into  form  for  transmission. 

3.  Transmission  of  power. 

4.  Utilization  of  power. 

An  analysis  of  the  first  three  items  is  shown  in  Table  II.  In 
Table  III  is  shown  the  ordinary  maximum  and  minimum  ef- 
ficiencies obtained  from  various  motors  and  machines  in  prac- 
tical work.  Higher  efficiencies  are  sometimes  obtained  under 
test  conditions  where  great  attention  is  given  to  secure  favorable 
conditions,  and,  in  many  places  where  careless  work  is  permitted, 
neglect  and  unsatisfactory  conditions  will  result  in  much  lower 
efficiencies  than  the  minimum  shown. 

23.  The  Losses  in  a  Hydro-electric  Plant. — To  emphasize  and 
point  out  in  greater  detail  the  various  losses  encountered  in  the 
generation  and  transmission  of  energy,  especially  as  applied  to 
hydro-electric   plants,   attention    is   called   to   Fig.    16.      In   this 
diagram  is  traced  the  losses  from  the  potential  energy  of  the 
water  in  the  head  race  of  the  power  plant  to  the  power  avail- 
able at  the  point  where  it  is  used.     In  each  case  considered  it  is 
assumed  that  1,000  horse-power  of  energy  is  applied  to  the  par- 
ticular work  considered. 

First,  consider  the  transmission  of  power  for  traction  pur- 
poses. If  a  certain  head  is  available  when  no  water  is  flowing 
in  the  raceways,  that  head  becomes  reduced  at  once  when  the 
wheels  begin  to  operate.  A  certain  amount  of  head  is  also  lost 
in  order  to  overcome  the  friction  of  flow  through  raceways,  racks 
and  gateways.  In  the  problem  here  considered  it  is  assumed 
that  the  above  losses  are  five  per  cent,  of  the  total  energy  avail- 
able in  the  head-race,  and  that  this  loss  occurs  before  the  water 
reaches  the  turbines:  hence,  95  per  cent,  of  the  potential  energy 
is  available  at  the  turbine.  The  turbine  loss  is  here  assumed  to 
be  about  20  per  cent.  First-class  turbines  under  three-quarter 
to  full  load  conditions,  will  commonly  give  80  per  cent,  efficiency, 
or  a  little  better. 

Professor  Unwin,  in  his  "Development  and  Transmission  of 
Power,"  page  104,  gives  the  following  percentage  of  loss  in  tur- 
bines: 


The  Losses  in  a  Hydro-Electric  Plant. 


27 


Shafting,  friction  and  leakage 3  to    5  per  cent. 

Unutilized  energy 3  to    7  per  cent. 

Friction  in  shaft,  guides  and  passages ' 10  to  15  per  cent. 

Total  loss  of  energy 16  to  27  per  cent. 

TABLE  II. 

Method  of  Generation.  Losses. 

(            r                         Internal  Combustion  Engine 
^  Gas — Oil Engine  losses. 

Fuel (Direct  (Vacuum  Pump)   (  Furnace. 

Steam  j  \  Boiler. 

Fn  (  Indirect (  Piping. 

f  Direct  (Ram) Ram  losses. 

S  g    j  Water          ! 

g<2          Power..  1  indirect  (Wheels) 

a  f  Electric  (Primary  Batteries) . . .  [  Various    mechani- 

§  Minor          j  Wind  (Mills) I      cal  and  other 

O  Sources .    j  Waves  (Motors) ]      losses  due  to 

[ Sun  Heat  (Solar  Engines) [     method  used. 

g        f  Internal  Combustion  Engine Included  in  engine 

§   •  losses. 

rv,    £* 

rM    Q 

g|       Steam Engine' and    con- 

g  g  nection  losses. 

Electrical Dynamos  and  wire 

«i  H  losses. 

^    rv* 

x  g       Hydraulic Pump  losses. 

°       I  Pneumatic Compressor  losses . 

,  f  Di rect  connected,—  Shaft f 

Mechan-  j  Cables,  Ropes,  Chains )  Various  losses  due 

ical Electric ]      to  method  used. 

^  [Combination I 

o 

I  f  Entrance  head. 

j  Pipe  friction. 

g         Hydraulic *j  Motor  losses. 

^  L  Connections. 

H     . 

fTranformer  losses, 

j  Wire  losses. 
g         Electrical 1  Motor  losses. 

[Connections. 

[Pipe  friction. 
J  Air  cooling. 

Pneumatic "j  Motor  losses. 

I  1  Connections. 


Power. 


The  Losses  in  a  Hydro-electric  Plant.  29. 

The  next  loss  shown  on  the  diagram  is  the  loss  in  transmitting 
the  energy  through  the  bevel  gear  and  the  shafting  to  the  gen- 
erator. The  loss  in  gearing,  shafting,  etc.,  is  shown  as  10  per 
cent.,  which  is  probably  much  less  than  actually  takes  place  in- 
most plants  of  this  kind,  but  may  be  considered  as  representing 
the  results  of  good  practice. 

The  loss  in  the  transformation  of  power  in  the  generator  is- 
given  as  8  per  cent.  The  generator  is  an  alternator,  and  the  cur- 
rent generated  would  be  at  about  2,300  volts.  This  current  must 
be  raised  to  a  higher  voltage,  by  means  of  transformers,  for 
long  distance  transmission.  These  transformers  would  give  an 
efficiency  of  about  96  per  cent.  The  line  loss  is  dependent  on  the 
size  of  the  copper  used,  but  would  probably  not  exceed  10  per 
cent.  At  the  distributing  point,  where  the  energy  is  to  be  used,, 
the  high  voltage  current  must  be  transformed  again  into  suit- 
able voltage  for  distribution.  The  same  energy  loss  is  estimated 
for  these  transformers.  If  the  current  is  to  be  used  for  traction 
purposes,  it  will  be  necessary  to  convert  it  into  direct  current 
by  means  of  a  rotary  converter,  the  efficiency  of  which  is  esti- 
mated at  92  per  cent.  The  voltage  from  the  general  distribution 
system  would  probably  be  too  high  for  direct  use  in  the  rotary 
converter,  and  would  have  to  be  transformed  to  a  lower  voltage 
before  passing  into  the  converter.  A  loss  of  about  6  per  cent., 
therefore,  should  be  allowed  for  this  transformation. 

The  current  from  the  rotary  converter  is  subject  to  a  line  loss- 
which  may  be  again  assumed  at  10  per  cent.  The  loss  in  the  car 
motor  may  be  estimated  at  7  per  cent.  The  percentage  of  loss 
and  the  percentage  of  efficiency  for  each  unit  in  this  generation 
and  transmission  system  is  based,  of  course,  on  the  actual  energy 
supplied  and  the  unit  next  previous  to  it  in  the  system,  so  that 
the  percentages  mentioned  are  not  based  on  the  total  potential 
power  available  in  the  head-race  but  on  the  power  actually  reach- 
ing the  machine. 

In  the  solution  of  any  actual  problems  of  this  character  it  is 
necessary  to  determine  the  efficiencies  of  the  various  units  of 
the  plant  under  the  condition  of  actual  service.  The  efficiency 
will  be  found  to  vary  under  various  conditions  of  load.  It  may 
therefore  be  desirable  to  determine  the  probable  losses  under 
various  working  conditions. 

In  the  selection  of  the  various  machines  which  are  to  form  a. 
part -of  such  a  system  of  transmission,  the  choice  should  be 


Power. 


based  on  an  effort  to  establish  a  plant  which  will  give  the  maxi- 
mum economy  when  all  conditions  of  loading  are  considered. 
The  losses  in  the  transmission  of  power  for  traction  purposes, 
as  shown  on  the  diagram,  may  be  traced  through  in  tabular 
form  as  follows : 


TOTAL  ENERGY 
AVAILABLE. 

1,000  HORSE 
POWER. 

Per  Cent 
Loss. 

Per  Cent 
Efficiency. 

Loss  in 
horsepower 

5 

20 
10 
8 
4 
10 
4 
6 
8 
10 
7   . 

95 
80 
90 
92 
96 
90 
96 
94 
92 
90 
93 

50 
190 
76 
54.7 
25.2 
60.4 
21.  7 
31.3 
39.3. 
45.1 
28.4 

Shaft  and  2T69.ri.nsr                       . 

Generator                  

Transformers  

Transmission  line  

Step-down  Transformers  

Secondary  Transformers 

-Rotary  Converters 

Line                    ....           .                   .  . 

Traction  Motor  -  

Power  utilized  for  operating  the  cars,  or  37£  per  cent   of  the 
original  energy 374.5  Horse  Power. 

In  the  generation  and  transmission  of  power  for  lighting  pur- 
poses, the  losses  will  be  similar  to  those  above  mentioned,  up 
to  and  including  the  step-down  transformers  at  the  point  of  dis- 
tribution. In  this  case,  however,  no  secondary  transformers  or 
rotary  converters  would  be  necessary.  The  only  loss  between 
the  step-down  transformers  and  the  light  will  be  the  line  loss 
assumed  at  5  per  cent.  The  loss  in  the  individual  transformer 
for  the  light  will  be  about  8  per  cent.,  leaving  the  available  en- 
ergy for  actual  use  in  the  lamp  at  about  456.2  horse  power,  or  a 
little  less  than  46  per  cent.,  of  the  total  energy  in  the  head-race. 

In  the  case  of  the  utilization  of  this  energy  for  manufacturing 
purposes,  the  loss  would  be  the  same  up  to  and  including  the 
step-down  transformers  at  the  point  of  distribution.  The  line 
loss  in  the  distribution  from  the  transformer  house  to  the  manu- 
facturing establishment  may  be  assumed  at  5  per  cent.  The 
motor,  if  properly  selected,  may  be  run  at  the  line  voltage,  and 
no  transformer  losses  need  be  considered.  The  motor  efficiency 
is  here  shown  at  92  per  cent.,  although  in  most  cases  the  per- 
centage of  efficiency  would  be  considerably  less. 

The  belt  loss  in  transmitting  the  power  from  the  motor  to  the 
line  shafting  is  estimated  at  5  per  cent. 


Efficiency  of  Generators  and  Motors. 
TABLE  III. — Ordinary  Efficiency  of  Generators  and  Motors. 


CLASS  OF  MACHINERY. 

EFFICIENCY  PER 
CENT  AT  FULL 
LOAD. 

Maxi- 
mum. 

Mini- 
mum. 

Water  Wheels  

f  Overshot  Wheels  

75 
05 

40 
85 
85 

75 
95 

18 
15 
12 
12 

12 

9 
9 

7 

7 

'     20 
30 

12 
9 
6 
4.5 
3 

50 
70 

92 
90 
85 
95 

95 
97 
95 
99 
95 
85 
75 

97 
98 
95 

65 
60 
25 
60 
75 

50 
75 

15 
12 

10 
10 

10 
7 
7 
6 
5 

16 
25 

10 
7 
5 
3 
2 

30 
60 

80 
80 
75 
50 

85 
90 
75 
95 
70 
50 
50 

92 
90 

85 

Breast  Wheels  

^  Undershot  Wheels  

Turbines 

(.  Impulse  Wheels 

Boilers  

Steam  Generators.  ,  

Condensing  ) 
Steam  Engines  .  \  " 

Non-Condensing  ) 
Steam  Engines.  .  ) 

f  Triple  Expansion  Corliss  

i  Compound  Corliss        

Simple  Corliss  ...           

i.  Compound  High  Speed  

f  Compound  Corliss  

Simple  Corliss 

\  Compound  High  Speed 

Simple  Hi^h  Speed 

[.Simple  Slide  Valve           .   . 

(  Gas  or  Oil  Engines  

Steam  Air  Compression  .  . 

/  Diesel  Motor  

f  Compound  Con  Corliss 

Simple  Con  Corliss 

•{  Simple  Corliss  

High  Pressure     

[^  Small  Straight  Line  

j  Air,  cold  

Electrical  Machinery  

Transmitting  Mechan- 
isms   

Air  reheated  

f  Dymimos          

'  Motor  large  

1  Motor  small  

I  Transformer 

CBelt  

Rope         

Cable         

j  Direct  connection 

Transmission  Methods.. 

Shafting  

Gearing  

1  Bevel  Gearing  

(  Pneumatic  per  mile 

•]  Hydraulic  per  mile 

(  Electric  usual    

32  Power. 

The  shafting  necessary  for  the  general  distribution  of  power 
through  the  factory  is  estimated  at  75  per  cent,  efficiency. 

The  belt  loss  from  the  shaft  to  the  individual  machine  is  esti- 
mated at  an  additional  5  per  cent.,  leaving  the  total  energy  avail- 
able for  use  in  the  machine  at  308.8  horse  power,  or  about  31  per 
cent,  of  the  original  energy  in  the  head-race. 

It  should  be  noted  that  in  each  of  the  three  transmission  sys- 
tems mentioned  above,  the  actual  power  utilized  at  the  point  of 
application  is  less  than  half  of  the  energy  available  in  the  head- 
race. It  is  the  function  of  the  engineer  to  see  that  these  losses 
are  reduced  to  the  greatest  practicable  extent.  These  losses 
must  be  limited  in  both  directions.  They  must  not  be  too  great, 
nor  too  small.  They  must  be  adjusted  at  the  point  where  true 
economy  would  dictate.  This  limit  is  the  point  where  the  cap- 
italized value  of  the  annual  power  lost  is  equal  to  the  capitalized 
cost  of  effecting  further  saving.  In  other  words,  true  economy 
means  the  construction  of  a  plant  that  will  save  all  the  power 
or  energy  which  it  is  financially  desirable  to  save,  and  will  per- 
mit such  waste  of  energy  as  true  economy  directs. 

24.  Units  of  Energy. — Energy  is  known  by  many  names  and 
exists  in  many  forms  which  seem  more  or  less  independent.  The 
principal  forms  of  energy  are  measured  by  various  units.  Those 
most  commonly  considered  in  power  development  and  trans- 
mission are  as  follows: 

Work  is  energy  applied  to  particular  purposes.  In  general  it 
is  energy  overcoming  resistance,  mechanically  it  is  the  exertion 
of  force  through  space. 

Power  is  the  rate  of  work,  or  the  relative  amount  of  work  done 
in  a  given  space  of  time. 

The  unit  of  work  is  the  foot  pound,  or  the  amount  of  worx: 
.required  to  raise  one  pound  one  foot.  One  pound  raised  one 
foot,  one-tenth  pound  raised  ten  feet,  ten  pounds  raised  one- 
tenth  of  a  foot,  or  any  other  sub-division  of  pounds  and  feet 
whose  product  will  equal  one  requires  one  foot-pound  of  work 
to  perform  it. 

The  unit  of  power  is  based  on  the  unit  of  work,  and  is  called 
"horse  power."  It  is  work  performed  at  the  rate  of  550  foot 
pounds  per  second,  or  33,000  foot  pounds  per  minute. 

Units  of  Heat.  The  unit  of  heat  is  the  amount  of  heat  which 
will  raise  one  pound  of  water  from  39  degrees  Fahr.  to  40  degrees 
Fahr.  at  atmospheric  pressure.  It  is  called  the  British  Thermal 
Unit,  and  is  indicated  by  the  initials  B.  T.  U. 


Conversion  of  Energy  Units.  33 

Electric  Unit.  The  unit  of  quantity  of  electricity  is  the  coulomb. 
One  coulomb  per  second  is  called  an  ampere,  and  one  ampere  un- 
der a  volt  pressure  is  equal  to  a  watt,  the  unit  of  electric  power. 

Water  Power.  Water  power  is  the  power  obtained  from  a 
weight  of  water  moving  through  a  certain  space.  In  water  power 
the  unit  of  quantity  may  be  the  gallon  or  the  cubic  foot ;  the  unit  of 
head  may  be  the  foot ;  and  the  unit  of  time  may  be  the  second  or 
minute.  The  weight  of  water,  unless  highly  mineralized,  at  ordi- 
nary temperature,  varies  from  62.3  to  62.5  pounds  per  cubic  foot. 
As  these  weights  vary  from  each  other  less  than  one-third  of  one 
per  cent.,  the  difference  is  insignificant  in  practical  problems  where 
the  errors  and  uncertainties  are  often  large.  In  the  further  discus- 
sion of  this  subject,  therefore,  the  weight  of  62.5  pounds  is  used  as 
the  most  convenient  in  calculation. 

Steam  Pozver.  The  unit  of  steam  power  in  ordinary  use  is  the 
pound  of  steam,  its  pressure,  and  rate  of  use.  It  is,  however,  based 
on  the  heat  unit,  and  must  be  so  considered  for  detailed  examina- 
tion. 

Definite  quantities  of  work  are  also  designated  by  the  "horse 
power  hour,"  equivalent  to  1,980,000  foot  pounds,  and  the  "kilowatt 
hour,"  equivalent  to  2,654,150  foot  pounds. 

The  pound  of  steam  may  be  considered  as  containing  an  aver- 
age of  1,000  British  thermal  units,  which  may  be  utilized  for  power. 
This  is  equivalent  to  778,000  foot  pounds. 

25.  Conversion  of  Energy  Units, — The  various  forms  of  energy 
as  expressed  by  the  units  named  are  convertible  one  into  another  in 
certain  definite  ratios  which  have  been  determined  by  the  most 
careful  laboratory  methods.  In  considering  these  ratios,  however, 
it  must  be  remembered  that,  as  shown  in  the  preceding  examples, 
in  the  transformation  from  one  form  of  energy  into  another  the 
ratios  given  cannot  be  attained  in  practice  on  account  of  losses 
which  can  not  be  practically  obviated.  Such  losses  must  be,  in 
good  practice,  reduced  to  a  minimum,  and  the  ratios  given  are, 
therefore,  the  end  or  aim  toward  which  good  practice  strives  to  at- 
tain as  nearly  as  practicable  when  all  conditions  and  facts  are  duly 
considered. 

Energy  must  be  considered  in  two  conditions  as  well  as  in  the 
above  named  forms,  viz. :  passive  and  active  or  potential  and 
kinetic. 

Potential  energy  is  energy  stored  and  does  not  necessarily  in- 
volve the  idea  of  work.  Kinetic  energy  is  energy  in  action  and 
8 


34  .Power. 

involves  the  idea  of  work  done  or  power  exerted  and  for  its  meas- 
urement must  be  considered  in  relation  to  time. 

The  most  common  units  of  potential  energy  and  their  equiva- 
lents are  as  follows : 

The  footpound  (one  pound  raised  one  foot). 

=1/62.5  or  .016  foot  cubic  foot  (of  water). 
=1/8.34  or  .12  foot  gallon  (of  water). 
=1/2655.4  or  .0003766  volt  coulombs. 
=1/778  or  .001285  British  thermal  units. 

The  foot  cubic  foot  (one  cubic  foot  of  water  raised  one  foot) . 
=62.5  foot  pounds. 
=7.48  foot  gallons. 
=.08  British  thermal  units. 
=.02353  volt  coulombs. 

The  foot  gallon  (one  gallon  of  water  raised  one  foot) 
=8.34  foot  pounds. 
=.01072  British  thermal  units 
=.00314  volt  coulombs. 
=.1334  foot  cubic  feet. 
The  volt  coulomb 

=2655.4  foot  pounds. 
=42.486  foot  cubic  feet. 
=318.39  foot  gallons. 
=3.414  British  thermal  units. 
The  British  thermal  unit 
=778  foot  pounds. 
=12.448  foot  cubic  feet. 
=93.28  foot  gallons. 
=.2929  volt  coulombs. 

Quantities  of  energy  available,  used  or  to  be  used,  and  either 
potential  or  kinetic  may  be  measured  in  the  above  units. 

When  the  rate  of  expenditure  is  also  stated  these  units  express 
units  of  power.     Some  of  the  equivalent  values  of  power  are  as  fol- 
lows, those  most  commonly  used  being  printed  in  black-face  type: 
The  horse  power 

=1980000  foot  pounds  per  hour. 
=33000  foot  pounds  per  minute. 
=550  foot  pounds  per  second. 
=31680  foot  cubic  feet  per  hour. 
=528  foot  cubic  feet  per  minute. 


Conversion  of  Energy  Units.  35 

=8.8  foot  cubic  feet  per  second. 

=237600  foot  gallons  per  hour. 

=3960  foot  gallons  per  minute. 

=66  foot  gallons  per  second. 

=746  watts. 

=2545  British  thermal  units  per  hour. 

=42.41  British  thermal  units  per  minute. 

^=.707  British  thermal  units  per  second. 

The  foot  pound  per  minute 

=1/33000  or  .0000303  horse  power. 

=1/778  or  .00129  British  thermal  units  per  minute. 

=.0226  watts. 

=i/8.34=.i2  foot  gallons  per  minute. 

=i/62.5=.oi6  foot  cubic  feet  per  second. 

The  foot  cubic  foot  per  minute 
=62.5  foot  Ibs.  per  minute. 
=i/528=.ooi89  horse  power. 
=1.412  watts. 

=7.48  foot  gallons  per  minute. 
=.0803  British  thermal  units  per  minute. 

The  foot  cubic  foot  per  second 

=375°  f°ot  ft>s-  Per  minute. 
=62.5  foot  Ibs.  per  second. 
=i/8.8=.  1 1 36  horse  power. 
=448.8  foot  gallons  per  minute. 
=7.48  foot  gallons  per  second. 
=4.820  British  thermal  units  per  minute. 
=.0803  British  thermal  units  per  second. 
The  watt 

=44.24  ft.  Ibs.  per  minute/ 

=.00134  horse  power. 

=.0568  British  thermal  units  per  minute. 

=5.308  gallons  feet  per  minute. 

=.7089  ft.  cu.  ft.  per  minute. 

The  British  thermal  units~pef" rrrrirute 
=778  ft.  Ibs.  per  minute. 
=.02357  horse  power. 
=17.58  watts. 
=93.28  ft.  gal.  per  minute. 
=12.48  ft.  cu.  ft.  per  minute. 


36  Power. 

26.  Motion  in  General.  —  In  moving  a  body  against  a  given  force  or 
resistance  the  work  done  in  foot  pounds  is  the  product  of  the  space 
passed  through  (in  feet)  and  the  resistance  (in  pounds).  Thus  in 
raising  a  ten-pound  weight  100  feet  high,  1,000  foot-pounds  of  work 
is  performed.  But  this  is  not  the  only  work  performed.  To  pro- 
duce motion  in  a  body  or  to  bring  a  body  to  a  state  of  rest  neces- 
sitates a  transfer  of  energy.  For  all  moving  bodies  are  endowed 
with  kinetic  energy  —  the  energy  of  motion  —  and  this  energy  must 
be  given  to  them  to  produce  motion,  and  must  be  taken  from  them 
to  produce  a  state  of  rest. 

Hence,  Newton's  laws  of  motion: 

1.  "Every  body  continues  in  a  state  of  rest,  or  of  uniform  mo- 

tion in  a  straight  line  except  in  so  far  as  it  may  be  com- 
pelled by  impressed  forces  to  change  that  state." 

2.  "Change  of  motion  is  proportional  to  the  impressed"  force 

and  takes  place  in  the  direction  of  the  straight  line  in 
which  the  force  acts." 

3.  "To  every  action  there  is  always  an  equal  and  contrary  reac- 

tion." 

The  acceleration  of  gravity  is  the  acceleration  due  to  the  weight 
of  a  body  acting  on  its  mass. 

The  weight  of  a  body  W  (on  account  of  centrifugal  effect  of  the 
earth's  revolution)  varies,  being  least  at  the  equator  and  greatest 
at  the  poles.  From  Newton's  second  law  it  follows  that  the  accel- 
eration in  motion  designated  by  g  and  caused  by  the  weight  of  any 
body  acting  on  its  mass  will  be  proportional  to  its  weight,  i.  e.,  g^= 
constant  X  W,  and  hence  the  weight  of  a  body  divided  by  the  ac- 
celeration will  always  be  constant.  This  constant  quotent  desig- 
nated by  the  letter  M  is  termed  the  mass  of  the  body. 

(:)M=|- 

LetW=The  weight  of  a  body. 


g=Acceleration  due  to  gravity=velocity  of  a  falling  body  at 
end  of  first  second,  and  is  ordinarily  taken  as  32.2  ft. 
per  sec.  per  sec. 

A=Acceleration  of  moving  body=velocity  of  body  at  end 
of  first  second. 

W'=Weight  acting. 

W"=Weight  acted  on. 


Kinetic  Energy.  37 

V=  Velocity  at  end  of  time  t. 

Va—  Average  velocity. 

t=Time  force  has  acted. 

S=Space  passed  through. 

h=Height  passed  through  by  falling  body. 

V'=Initial  velocity. 

S'=Initial  space  passed  through. 

27.  Uniform    Motion.  —  In    uniform    motion    the    moving    body 
passes  through  equal  spaces  in  any  equal  divisions  of  time. 

Hence  by  definition  : 

The  space  passed  through  (S)  equals  the  product  of  the  velocity 
(V)  and  the  time  (t). 

(2)  S=Vt. 

(3)  VA 

28.  Uniformly  Varied  Motion.  —  If  the  velocity  of  a  body  is  in- 

creased or  diminished  uniformly,  the  motion  is  termed  uniformly 
varied  motion  and  is  termed  uniformly  accelerated  motion  in  the 
first  case  and  uniformly  retarded  motion  in  the  latter  case. 
In  all  such  cases  the  following  relations  hold: 

' 


(5)  V=At=g  t. 

(6)  Va=Al 


(8)  V=VTA~S. 

ith  falling  bodies  : 

S=h, 
A=g. 
From  which  equation   (8)  becomes 

(9)   V=V  2  gh,  tne  we^  known  basis  of  hydraulic  calcu- 

lations. 
(10)  Worfc=W  h=W  VV2ff=M  V/2. 

29.  Compound  Motion.  —  When  bodies  are  already  in  motion  and 
additional  force  is  applied,  the  following  relations  hold  : 

(i  i)  V=V'+At. 
(12)   S= 


Power. 


30.  Graphical  Representation  of  the  Laws  of  Motion. — In  each 
case — 

The  vertical  ordinates  represent  velocity 

Abscissas  represent  time. 

Areas  represent  space  passed  through. 


TIME 
UNIFORM         MOTION 


UNIFORM        ACCELERATED       MOTION 


V   =  constant 

S  =  Vt 


V  =  At  =         gt 


v  f       At2         V» 
sV»t:=    T     :    2A 

V  =  T/2AS" 


V  =  V  +  At 

S-  S'  +  V  t 


COMPOUND         MOTION    - 

WITH        INITIAL. 


ACCELERATED. 
VELOCITY 


Fig.  17. — Graphical  Representation  of  the  Laws  of  Motive. 

31.  Transformation. — The  transformation  of  potential  to  kinetic 
energy  is  well  illustrated  by  water  acting  upon  a  water  wheel.  The 
energy  in  a  body  is  always  constant  whatever  its  form,  except'  as 
said  energy  be  given  up  to  other  bodies  or  lost  and  wasted  in  vari- 
ous ways.  Consequently  the  sum  of  the  potential  and  kinetic  en- 
ergies in  any  body  is  a  constant  quantity  unless  the  difference  be 
accounted  for  by  energy  loss  or  transfer  as  above  noted. 

Water  that  has  fallen  to  sea  level  has  lost  all  the  energy  it  may 
have  once  possessed,  its  energy  having  been  expended  in  perform- 
ing some  kind  of  work. 

If,  in  a  hydraulic  plant,  we  have  an  available  fall  of  8.8  ft.  every 
cubic  foot  of  water  passing  through  this  distance  each  second  pro- 
duced 33,000  ft.  Ibs.  of  work,  or  one  horse  power.  After  the  water 
has  passed  through  a  well-designed  turbine  it  flows  sluggishly 
away,  having  used  up  nearly  all  its  energy  in  the  turbine  to  which 


Literature.  39 

it  has  transferred  its  energy.  If,  however,  on  account  of  bad  de- 
sign the  water  flows  away  at  a  rapid  rate,  say  at  10  feet  per  second, 
the  head  lost,  h=v2/2g  i.  e.  h=io2/6"44=i.55  ft.  of  vertical  fall. 
Under  these  conditions  the  energy  due  to  this  fall  still  remains  in 
the  water,  after  it  has  left  the  wheel,  and  is  lost,  the  loss  being 
17.8  per  cent,  of  the  original  energy. 


LITERATURE. 

1.  Thurston,  Robert  H.     Conversion  Tables  of  Weights  and  Measures.   New 

York.    J.  Wiley  &  Sons.    1883. 

2.  Oldberg,  Oscar.     A  Manual  of  Weights  and  Measures.     Chicago.     C.  J. 

Johnson.     1887. 

3.  Everett,  J.  D.    Illustrations  of  the  C.  G.  S.  System  of  Units.    New  York. 

MacMillan  &  Co.     1891. 

4.  Anderson,  William.     On  the  Conversion  of  Heat  into  Work.     Discussion 

of  energy  conversion.     London.     Whittaker  &  Co.     1893. 

5.  Unwin,  W.  C.     On  the  Development  and  Transmission  of  Power.     Long- 

man &  Co.    London.    1894. 

G.  Oswald,  Wilhelm.     Manual  of  Physics,  —  Chemical  Measurements.     New 
York.     The  MacMillan  Co.     1894. 

7.  Peabody,  Cecil  H.     Tables  of  the  Properties  of  Saturated  Steam.     New 

York.     J.  Wiley  &  Sons.     1895. 

8.  Richards,  Frank.     Compressed  Air.     New  York.     J.  Wiley  &  Sons.     1895. 

9.  Bolton,  Reginald.     Motive  Powers  and  Their  Practical   Selection.     New 

York.     Longmans,  Green  &  Co.     1895. 

LO.  Holman,  Silas  W.     Matter,  Energy,  Force  and  Work.     New  York.     The 
MacMillan  Co.     1898. 

11.  Kent,   Wm.     Notes   of  the   Definition   of   Some  Mechanical   Units.     Am. 

Asso.  Adv.  of  Sci.     1898.     See  also  Eng.  News,  Vol.  40,  p.  348. 

12.  Mead,   Daniel   W.     Commercial   Transformation   of  Energy.     Trans.    111. 

Soc.  Eng.     14th  report,  1899. 

13.  Reeve,   Sidney  A.     The   Steam  Table.     New  York.     The  MacMillan  Co. 

1903. 

14.  Kohlrausch,  F.     An  Introduction  to  Physical  Measurements.     New  York. 

D.  Appleton  &  Co.     1903. 

15.  Carpenter,   R.   C.     Experimental  Engineering.     New    York.     John    Wiley 

&  Sons.    1903. 

16.  Herwig,  Carl.    Conversion  Factors.    New  York.    J.  Wiley  &  Sons.     19u4. 

17.  Smithsonian  Institution.     Physical  Tables.     3d  Edition.     1904. 

18.  American  Institute  of  Electrical  Engineering.     Report  of  Committee  en 

Standardization.    1907.    Proc.  Am.  Inst.  E.  E.  Vol.  26,  pp.  1076- 
HOG. 


CHAPTER  III. 

HYDRAULICS. 

32.  Basis  of  Hydraulics. — The  science  of  hydraulics  is  an  empir- 
ical, not  an  exact  science,  but  is  based  on  the  exact  sciences  of 
hydrostatics  and  dynamics.  Its  principal  laws  are  therefore  founded 
on  theory,  but  on  account  of  the  multitude  of  modifying  influences 
and  of  our  necessarily  imperfect  theoretical  knowledge  of  their 
varying  characters  and  extent,  the  formulas  used  must'  be  derived 
from  or  at  least  modified  by  observation  and  experience  and  can- 
not be  founded  solely  on  theoretical  considerations.  The  condi- 
tions under  which  hydraulic  laws  must  be  applied  are  so  varied  in 
both  number  and  kind  that  the  application  of  the  laws  must  be 
modified  to  suit  those  various  conditions  and  for  this  reason  their 
successful  application  depends  largely  on  the  practical  experience 
of  the  engineer. 

In  the  following  discussion  the  letters  used  will  have  the  signifi- 
cance shown  below : 

E=Energy   (abstract). 

P=Horse  power. 

W=Total  weight  of  water. 

h=The  total  available  head  in  feet. 

hx=The  velocity  head. 

h2=The  entrance  head  or  influx  head. 

h3=The  friction  head. 

q=The  quantity  of  water  (in  cubic  feet  per  second). 

w— The  weight  of  each  unit  of  water  (cu.  ft.=62.5  Ibs.). 

a=Area    (in  square  inches)    against  which   pressure  is   ex- 
erted. 

s=The  space  (in  lineal  feet)  through  which  the  area  moves 
under  pressure. 

v=The  velocity  of  flow  (in  feet  per  second). 

^^Acceleration  due  to  gravity  (32.2  feet  per  second  per  sec- 
ond.) 

t=The  time  in  seconds. 

33.  Mathematical  Expression  for  Energy. — Mechanically,  energy 
is  the  exertion  of  force  through  space.  The  amount  of  available 


Mathematical  Expression  for  Energy.  41 

energy  of  water  that  may  be  theoretically  utilized  is  measured  by 
its  weight  (the  force  available)  multiplied  by  the  available  head 
(the  space  through  which  the  force  is  to  be  exerted),  i.  e.,  (i)  E= 
Wh.  From  this  it  will  be  noted  that  the  energy  of  water  is  in 
direct  proportion  to  both  the  head  and  quantity.  This  energy  may 
be.  exerted  in  three  ways  which  may  be  regarded  as  more  or  less 
distinct  but  which  are  usually  exercised,  to  some  extent  at  least. 
in  common.  The  exertion  of  this  energy  in  the  three  ways  men- 
tioned, expressed  in  terms  of  horse  power,  are  as  follows  : 

First:  By  its  weight  which  is  exerted  when  a  definite  quantity 
of  water  passes  from  a  higher  to  a  lower  position  essentially  with- 
out velocity.  This  method  of  utilization  is  represented  by  the 
equation 


Second:  By  the  pressure  of  the  water  column  on  a  given  area 
exerted  through  a  definite  space.  This  method  of  utilization  is  rep- 
resented by  the  equation 

434h  as 


Third  :  By  the  momentum  of  the  water  exerted  under  the  full 
velocity  due  to  the  head.  The  energy  of  a  moving  body  is  repre- 
sented by  the  formula  : 

Wv2 

(4)  E  =  -^~ 

*g 

The  equation  for  the  horse  power  of  water  under  motion  is  there- 
fore represented  by  the  equation  : 


~  550  x  2g 

An  analysis  of  these  formulas  will  show  that  under  any  given 
conditions  the  theoretical  power  exerted  will  be  the  same  in  each 
case. 

34.  Velocity  Head  (hj).  —  It  has  already  been  pointed  out  (chap- 
ter IT)  that  energy  must  be  expended  in  order  to  produce  motion 
in  any  body  and  that  the  head  (hx)  necessary  to  produce  a  ve- 
locity (v)  is 


This  proportion  (hx/h)  of  the  available  head  h  has  to  be  ex- 
pended to  produce  and  keep  in  motion  the  flow  of  water.  This 
head  (hx)  is  not  necessarily  lost  (it  has  simply  been  converted  into 


42  Hydraulics. 

kinetic  energy,  and  it  may  be  re-converted  into  potential  energy  by 
correct  design  or  it  may  be  utilized  in  some  other  way,  as,  for 
example,  by  pressure  or  impact  in  hydraulic  motors). 

Whatever  head  (hx)  is  necessary  to  maintain  the  velocity  (v), 
with  which  the  water  leaves  the  plant,  will  be  lost  to  the  plant. 
It  is,  therefore,  desirable  to  keep  v  at  this  point  as  low  as  may  be 
found  practicable  when  other  conditions  are  considered. 

Sudden  enlargements  or  contractions  in  pipes  or  passages  may 
wholly  or  partially  destroy  the  velocity  and  cause  the  permanent 
loss  of  the  corresponding  head  (h±). 

In  this  case  an  additional  amount  of  the  available  head  (r^)  must 
be  used  to  again  generate  the  velocity  (v)  required  to  convey  the 
water  through  the  remainder  of  its  course.  Gradual  change  in  the 
cross-section  of  all  channel  conduits  or  passages  is,  therefore,  de- 
sirable in  order  that  the  transformation  from  kinetic  to  potential 
energy,  and  the  reverse,  shall  be  made  without  material  loss. 

Not  only  the  head  (hj)  but  still  other  portions  of  the  total  avail- 
able head  (h)  may  be  lost  in  the  channels  and  passages  of  a  ma- 
chine or  plant  by  improper  design. 

35.  Entrance  Head.  —  The  loss  of  head  (h2)  which  occurs  at  en- 
trance into1  a  raceway,  pipe  or  passage  may  be  called  the  "influx 
head."  The  amount  of  this  loss  differs  considerably  with  the  shape 
and  arrangement  of  the  end  of  the  pipe  or  passage.  In  general,  the 
influx  head  may  be  determined  by  the  formula: 

(7)  ha  =  (r  —  -(Merriman's  Hydraulics,  Art.  53) 


In  this  formula  the  coefficient  can  be  obtained  from  table  VI,  in 
which  the  variations  of  the  constant  under  various  conditions,  with 
reference  to  a  pipe  inlet,  are  shown,  and  from  which  it  will  be  noted 
that  its  magnitude  depends  on  the  shape  and  arrangement  of  the 
inlet. 

TABLE  IV. 
Arrangements  of  a  pipe  inlet  with  corresponding  coefficients. 


Arrangement  of  Pipe. 

c 

c8       l 

A.     Projecting  into  reservoir  

,715 

956 

B.    Mouth  flush  with  side  of  reservoir  

.825 

.469 

(from  

950 

108 

C.    Bell  shaped  mouth  (to  

990 

020 

Submerged  Orifices. 


To  find  the  value  of  h2,  the  value  of  -\-—  1  corresponding  to  the 

c 

given  conditions,  is  to  be  selected  from  Table  IV  and  substituted 
in  formula  (7).     The  ordinary  arrangement  of  suction  pipes  is  for 

a  square  ended  pipe  to  project  di- 
rectly into  the  suction  pit.  In  res- 
ervoirs the  pipe  may  be  flush  with 
the  masonry  or  project  as  in  the 
flcase  of  suction  pipes.  With  condi- 
tion (A)  formula  (7)  becomes 


(8) 


ha  =  .956-^ 

2g 


The  value  of  h2  can  be  readily 
obtained  from  equation  (8),  as  it 
will  be  95.6  per  cent,  of  the  veloc- 
ity head. 

With  the  mouth  of  the  pipe  flush 
with  the  side  of  the  reservoir  the 
loss  would  be  46.9  per  cent,  of  the 
velpcity  head,  and  with  a  bell 
mouth  pipe  the  loss  would  be  de- 
creased to  from  two  per  cent,  to 
10.8  per  cent,  according  to  the  de- 
sign of  the  bell  mouth  entrance. 

The  arrangements  of  inlet  pipes 
as  referred  to  in  Table  IV  are 
Fiz-  18.  shown  in  Fig>  Ig> 

36.  Submerged  Orifices. — A  similar  loss  is  sustained  in  the  flow- 
through  gates  or  submerged  openings  or  in  the  flow  past  any  form 
of  obstruction  which  may  be  encountered  by  the  water  in  its  flow 
through  channels,  pipes  or  other  forms  of  passages.  Openings  or 
obstructions  with  square  edges  may  cause  a  serious  loss  of  head 
which  may,  however,  be  reduced. 

First:  By  increasing  the  opening,  thus  causing  a  reduction  ini 
velocity  and  consequently  a  saving  in  head,  or 

Second :  By  rounding  the  corners  of  the  opening  or  obstruction, 
thus  causing  a  gradual  change  in  velocity  and  a  partial  recovery 
of  any  head  necessarily  used  for  creating  greater  velocity  through- 
such  passage  or  past  such  obstruction. 

But  few  experiments  have  been  made  on  submerged  orifices  and" 
tubes.  These  indicate  a  coefficient  of  about  .62  for  complete  con- 
traction which  increases  to  .98  or  even  .99  with  the  contraction* 


44  Hydraulics. 

completely  suppressed.  Certain  experiments  have  recently  been 
made  at  the  hydraulic  laboratory  of  the  University  of  Wisconsin, 
on  the  discharge  through  orifices  and  tubes  four  feet  square  and  of 
various  thicknesses  or  lengths  and  with  various  conditions  of  con- 
traction. The  values  of  the  coefficients  as  determined  in  these  ex- 
periments with  various  losses  of  head  and  various  conditions  of 
entrance,  are  shown  in  Table  V.* 

The  Forms  of  Entrance  and  Outlet  Used  for  the  Tubes  in  the  experiment 

were  as  follows:7 

A.     Entrance;  all  corners  90°. 

Outlet;  tube  projecting  into  water  on  down  stream  side  of  bulkhead. 
a    Entrance;  contraction  suppressed  on  bottom. 

Outlet;  tube  projecting  into  water  on  down  stream  side  of  bulkhead. 
b    Entrance;  contraction  suppressed  on  botton  and  one  side. 

Outlet;  tube  projecting  into  water  on  down  stream  side  of  bulkhead. 
c    Entrance;  contraction  suppressed  on  bottom  and  two  sides. 

Outlet;  tube  projecting  into  water  on  down  stream  side  of  bulkhead. 
c'  Entrance;  contraction  suppressed  on  bottom  and  two  sides. 

Outlet:  square  corners  with  bulkhead  to  sides  of  channel  preventing 

the  return  current  along  the  sides  of  the  tube. 
d    Entrance;  contraction  suppressed  on  bottom,  two  sides  and  top. 

Outlet;  tube  projecting  into  water  on  down  stream  side  of  bulkhead. 

From  this  table  it  will  be  noted  that  a  partial  suppression  of  con- 
traction does  not  always  improve  results,  and  that  by  complete  sup- 
pression, the  coefficient  is  greatly  increased  with  a  corresponding 
decrease  in  head  lost. 

37.  Friction  Head  (h3) — In  raceways  and  short  pipes  the  velocity 
head  (hi)  and  the  influx  head  (h2)  are  frequently  the  sources  of  the 
greatest  losses  of  head.  In  canals  and  pipes  of  considerable  length 
the  friction  of  flow  may  become  the  most  serious  sources  of  energy 
loss. 

The  principles  of  flow  in  such  channels  may  be  considered  as 
follows : 

First  Principle :  In  any  frictionless  pipe,  conduit,  channel  or  pas- 
sage of  unit  length  the  flow  may  be  expressed  by  the  formula : 

(9)  h  =  Y~  or  v  =  i/2gh~ 

In  practice,  however,  we  find  friction  is  always  present  and  a 
friction  factor  must  be  introduced  in  the  above  formula  in  order  to 


*From  experiments  by  Mr.  C.  B.  Stewart  at  the  Hydraulic  Laboratory  of 
the  University  of  Wisconsin. 


Friction  Head.  45 

represent  the  actual  conditions  of  practice.     (9)  therefore  becomes : 


(10) 


TABLE  V. 


Value  of  the  Coefficient  of  Discharge  for  flow  through  horizontal  submerged 
tube,  4  feet  square,  for  various  lengths,  losses  of  head  and  forms  of  entrance 
and  outlet. 


Loss  of 
head,  h2 
in  feet. 

Forms 
of  En- 
trance 
and 
Outlet 

Length  of  tube,  in  feet. 

i 
0.31 

0.62 

1.25 

2.50 

5.00 

10.0 

14.0 

Value  of  the  coefficient,  c. 

05  

A 

.631 

.650 

.672 

.769 

.807 

.824 

.838 

a 

.762 

.742 

.810 

.848 

b 

.740 

.769 

.832 

.862 

c 

.834 

.769 

.875 

.890 

c' 

.875 

d 

.948 

.943 

.940 

.927 

.931 

10       

A 

.611 

.631 

.647 

.718 

.763 

.780 

.795 

a 

.636 

.698 

.771 

.801 

b 

.685 

.718 

.791 

.813 

c 

.772 

.718 

.828 

.841 

c' 

.830 

d 

.932 

.911  • 

.899 

.892 

.893 

15  

A 

.609 

.628 

.644 

.708 

.758 

.779 

.794 

a 

.630 

.689 

.767 

.803 

b 

.677 

.708 

.787 

,814 

c 

.765 

.708 

.828 

.839 

c' 

.829 

d 

.936 

.910 

.899 

.893 

.894 

20        

A 

.609 

.630 

.647 

.711 

.768 

.794 

.809 

a 

.63;! 

.694 

.777 

.819 

b 

.678 

.711 

.796 

.833 

c 

.771 

.711 

.838 

.856 

c' 

.846 

d 

.948 

.923 

.911 

.906 

.905 

.25  

A 

.610 

.634 

.652 

.720 

.782 

.812 

.828 

a 

.634 

.705 

.790 

b 

.683 

.720 

.809 

c 

.779 

.720 

.854 

c' 

d 

.965 

.938 

.928 

30 

A 

.614 

.639 

.660 

.731 

.796 

.832 

.850 

-fi. 

a 

.639 

b 

.689 

c 

.788 

c' 

d 

.984 

46 


Hydraulics. 


The  formulas  (9)  and  (10)  represent  one  of  the  important  funda- 
mental principles  from  which  many  hydraulic  formulas  are  de- 
veloped. 

Second  Principle:  In  any  pipe,  conduit,  channel  or  passage  we 
may  fairly  assume: 

F«rst:  From  axiomatic  considerations  the  resistance  to  the  flow 
of  water  may  be  regarded  as  directly  proportional  to  the  area  of 
the  surface  in  contact  with  the  water. 

Second:  From  observed  conditions  the  resistance  is  found  to  be 
directly  proportional  to  the  square  of  the  velocity  of  flow. 

Third :  Experience  leads  to  the  conclusion  that  the  resistance  to 
flow  is  inversely  proportional  to  the  cross-section  of  the  stream. 

These  conclusions  may  be  expressed  by  the  following  equation: 

(Velocity)2X  area  of  contact 

Resistance  = y'      , : 

area  ot  section 


Fig.  19. 

The  area  of  the  surface  of  a  channel  is  the  product  of  the  wetted 
-section  or  wetted  perimeter  (p)  tirnes  the  length  of  the  section,  or, 
to  p  x  1.  (See  Fig.  19.)  The  velocity  is  represented  by  v  and  the 
cross-section  by  a.  Hence,  from  the  above  considerations,  we  may 
write  for  the  friction  head: 


(11) 


hs  =  — —  and  by  ;  transposition  va  =  — p 


That  is  to  say,  the  square  of  the  velocity  is  in  direct  proportion 
to  the  area  of  the  section  and  to  the  friction  head  and  inversely 
proportional  to  the  wetted  perimeter  and  to  the  length  of  the  sec- 
tion. 

In  practice  it  is  found  that  there  are  numerous  factors  which 


Kutter's  Formula.  47 

affect  the  theoretical  conditions,  as  above  set  forth,  which  must 
therefore  be  modified  in  accordance  with  the  conditions  which  ob- 
tain. In  formula  (n)  therefore  it  is  necessary  to  apply  a  coeffi- 
cient (c')  which  represents  the  summation  of  such  other  influences. 
The  form  in  which  this  last  equation  is  ordinarily  written  is 

/•ON  ,   v2pl  /ah, 

h"=C        a     0rV  =  CAfe- 

Ordinarily  this  form  is  somewhat  abbreviated  by  substituting-  for 
a/p  the  hydraulic  radius  which  represents  this  ratio.   That  is  to  say, 

area  of  cross  section  _    a 
wetted  perimeter       "  ^p~  " 

I  The  "hydraulic  radius"  is  also  sometimes  termed  the  "mean 
dfepth"  or  the  "mean  radius."  For  the  ratio  of  the  resistance  head 
to  the  length  of  section  the  equivalent  slope  s  is  substituted. 

That  is  to  say: 

Resistance  head          h3  _ 
Length  of   section  ~     1 

With   these   substitutions   the   formula    (12)    assumes   the   final 
fprm  of: 


(13)  v  = 

In  the  use  of  this  formula  three  factors  must  be  determined  by 
measurement  or  estimate  in  order  to  derive  the  fourth,  v,  r  and  s 
can  be  determined  experimentally  or  measured  directly.  The 
factor  c  is  the  most  difficult  to  ascertain  as  it  depends  upon  a  very 
great  variety  of  conditions  which  can  only  be  known  and  apprie- 
ciated  by  a  thorough  knowledge  of  the  conditions  under  considera- 
tion, and  by  comparison  of  such  conditions  with  similar  observed 
conditions.  Various  attempts  have  been  made  to  derive  a  formula 
which  would  give  the  value  of  c  in  accordance  with  the  varying 
conditions.  The  principal  formulas  for  the  values  of  c  are  those  of 
Ganguillet  and  Kutter  and  of  Bazin.  Ganguillet  and  Kutter's  form- 
ula for  the  value  of  c  is  as  follows  : 
|  38.  Kutter's  Formula.— 

41   fl    i     1'811  _,  0-00281 

>'...,."..         .....  4-L.p  -|  --  —  --  1-  —  ;•"  „    .  ,    ,    .        ,    •    , 


(14)  c  = 


From  this  formula  it  will  be  seen  that  Ganguillet  and  Kutter  as- 
sume c  to  vary  with  the  slope,  with  the  square  root  of  the  hydraulic 
radius  and  with  a  new  factor  "n"  which  is  termed  the  coefficient 


Hydraulics. 


HYPRAUL'IC    RADIUS  "r"- 

rf.      ,k 


1.0  2.0 

VELOCITY  V-  IN  FEET  PER  SECOND 


Fig.  20. 


Kutter's  Formula. 


49 


Fig.  21. 


50  Hydraulics. 

of  roughness.    The  value  of  this  coefficient  as  determined  by  these 

experiments  is  as  follows: 

For  large  pipe  with  the  following  characteristics: 

Exceptionally  smooth  cast  iron  pipe n  =  .on 

Ordinary  new  cast  iron  or  wooden  pipe .0125 

New  riveted  pipes  and  pipes  in  use .014 

Pipes  in  long  use .019 

For  open  channels  of  uniform  sections : 

For  planed  timber  sides  and  bottom 11=  .009 

For  neat  cement  or  glazed  pipe .01 

For  unplaned  timber  '. .012 

For  brick  work .013 

For  rubble  masonry .017 

For  irregular  channels  of  fine  gravel .02 

For  canals  and  rivers  of  good  section .025 

For  canals  and  rivers  with  stones  and  weeds  . . .  .030 

For  canals  and  rivers  in  bad  order 0.35 

The  relation  of  the  above  factors  may  be  determined  by  the  dia- 
grams, Figs.  20  and  21.  If  with  a  known  slope  and  a  known  value 
of  n  (for  example,  let  n=o.i5  and  s=.ooo2,  as  at  A,  Fig.  20),  a 
straight  line  be  drawn  on  this  diagram  to  the  scales  of  the  hydraulic 
radius  (at  B)  it  will  show  at  the  intersection  with  the  scale  for  the 
coefficient  (c)  the  relative  value  of  this  coefficient  for  these  condi- 
tions, or  with  a  known  c  and  the  known  hydraulic  radius  and  the 
given  slope  the  value  of  n  of  a  channel  may  be  likewise  determined. 
After  a  line  has  once  been  drawn  connecting  these  four  known 
values  the  velocity  can  be  determined  by  drawing  a  line  from  the 
hydraulic  radius  scale  (B)  to  the  proper  point  on  the  scale  of  slope 
or  hydraulic  gradient  at  x,  and  then  from  the  point  of  intersection 
of  the  line  A  B  with  the  coefficient  scale  at  x'  drawing  a  line  par-, 
allel  with  xB  which  will  intersect  the  velocity  scale  at  the  point  B', 
giving  the  velocity  (in  this  case  equal  to  1.34  ft.  per  second).  These 
formulas  only  apply  with  accuracy  where  the  channels  or  passages 
are  uniform  and  if  applied  to  channels  or  passages  which  are  not 
uniform  the  sections  selected  must  be  fairly  representative.  If  the 
sections  selected  are  not  fairly  representative  the  value  of  c  or  n 
determined  from  observations  and  experiments  may  vary  consid- 
erably from  the  values  which  would  otherwise  be  anticipated.  That 
is  to  say,  the*  calculations  based  on  c  and  n  will  take  into  account 
irregularities  in  channels  and  other  unknown  or  unrecognized  con- 
ditions, including  curves,  bends  and  obstructions  which  may  not 


Bazin's  Formula. 


Bazin's  Form 
value  of  c  in  th 

ula  fc 
e  for 
i  En 

7 

>r  the 
niuk 
glisl 

J 

L 
L 

I 

I 

I 

i  /  i  /i  / 

/  /    1 

/  /    fl 

/  /    / 

V 

n 

n 
n 

n 
n 

n 
n 

—  cv  rs  is,   n 
leasure, 

s 

/  /    / 

/  /    / 

M/    / 

c 

i-O 

552  + 

OGforsni( 
•  matchec 
10   for  p 
"ick. 
40  for  ma 
85  for  reg 
?ds. 
30    for    ( 
>od  order. 
75    in     \ 
der. 

m 

3tjL  m  nt 

l/r 
)oth  plant 
boards, 
anks  anc 

sonry. 
ular  eartt 

canals    in 
ery     bad 

n  I    /     1 

/N    / 

01 

1=0. 
bi 

/  /    / 

/  /    r      i 

/  /    1 

i  —  O. 
i=0 

/  /    H      \   \   \ 

b< 
1=1, 

gc 
i  —  I  . 

j 

ir          /            / 

/ 

JLLLA   IE    it 

/ 

/     /       / 

or 

/ 

/     I       / 

/ 

/ 

L  ji  j   n 

i 

/i  i/i  1  1  1 

/ 

1 

i 

/  on 

</ 

i 
7 

f 

T 

it  HTij 

j 

7 

3  1  "/Ir 

/ 

/ 

/ 

/ 

y     / 

, 

/  / 

/ 

/ 

z 

/  / 

/ 

/ 

^ 

v 

/       E 

(_  / 

' 

/ 

/ 

0     h 

7 

/ 

/ 

/ 

xl       /I 

/ 

/ 

X 

4^ 

[Z 

A 

^ 

X 

^^ 
^ 

~~  — 

_^—  — 

—  —  • 
— 

^  —  • 

—     — 

^^ 

„   — 

,--- 

^  — 

i 

if  N 

COEFFICIENT   V   IN     FORMULA     V  =  C/PT 
Fig.  22.—  Diagram" for; Solution  of  Bazin's  Formula. 


GRAPHICAL  SDLUTII 


v  -  c  \/~ 


V  =  VELDCITY    IN    FEET    PER    EECDND. 

C  "COEFFICIENT. 

R- HYDRAULIC    RADIUS    IN    FEET  =   -p- 

T" 


B  =  BINE    OF    SLDPE 


a=  AF 
p  =  w 
h=  F; 

I  =  LE 


VALU  E 


.4  .5         .8       .7      .B     .3    IB 


VELOCITIES       I 

Figu 


I  DF  CHEZYS  FORMULA 

s    =     I 

.IN    BQ.  FEET    OF    CHANNEL   SECTION 
FED    PERIMETER    DF    CHANNEL   SECTION    IN    LINEAL    FEET. 

IN    FEET    BETWEEN    POINTS   CONSIDERED. 
;TH    OR    DISTANCE, BETWEEN    POINTS   CONSIDERED,  IN    LINEAL    FEET. 

OF       R   .   5 


5  2.0  ES        3.Q  4,0  SQ        BD      7        BQ   g       ,Q          jg        ,         ,        j       2 


FEET     PER     SECOND 


54  Hydraulics. 

have  been  considered  at  the  time  the  original  observations  were 
made. 

39.  Bazin's  Formula. — It  has  been  questioned  by  many  observers 
whether  the  slope  of  the  channel  has  any  material  influence  on  the 
value  of  the  coefficient  c.     Bazin  has  derived  a  formula  based  on 
his  examination  of  this  subject  in  which  he  assumes  that  c  does  not 
vary  with  the  slope.    His  formula,  which  is  intended  for  the  calcula- 
tion of  flow  in  open  channels  is  shown,  together  with  a  graphical 
table  based  thereon,  in  Fig.  22.     This  figure  illustrates  the  law  of 
variation  of  c  and  is  applicable  in  principle  in  a  general  way  to  all 
channels  and  passages. 

The  graphical  diagram,  Fig.  23,  which  was  prepared  by  the  writer 
in  connection  with  Mr.  J.  W.  Alvord,  affords  a  ready  method  of 
solving  Chezy's  formula  (13). 

40.  Efficiency  of  Section. — From  equations  (12)  and  (13) 

v  =  c  T/^-  =  c  ^/^p 

(15)  q  =  velocity  X  area  =  va 

or  q  =  ca^/rs   =  ca,.  J— -? 

'  jo  3 

"With  c  and  s  constant  q  varies  as  a-/r      or  asA| — 

\p 

From  this  the  conclusion  may  be  drawn  that  other  things  being 
equal  the  maximum  quantity  of  water  will  pass  through  any  sec- 
tion of  any  river  or  other  channel  in  which  the  hydraulic  radius  is 
a  maximum  or  the  wetted  perimeter  a  minimum.  Where  a  choice 
exists  as  to  the  class  of  material  with  which  the  channel  is  to  be 
lined  c  becomes  a  variable  and  q  will  vary  as 

ca  i/r      or  as  c  *fi — 

That  is  to  say,  under  circumstances  where  different  characters  of 
lining  may  be  used  the  maximum  quantity  will  pass  a  given  sec- 
tion with  c  and  r  maximum  or  with  c  a  maximum  and  p  a  minimum 
for  given  a. 

41.  Determination  of  Canal  Cross-section. — The  velocity  of  the 
water  in  any  artificial  channel  must  be  limited  by  the  class  of  ma- 
terial used  in  its  construction  and  the  head  which  it  is  found  prac- 
ticable to  use.  As  noted  above  the  efficiency  of  a  section  is  greatest 
with  the  value  of  p  minimum.  Therefore,  the  semi-circular  sec- 
tion is  the  most  advantageous  cross-section  that  can  be  used  in  a 
channel  where  resistance  alone  is  considered  and  when  the  canal 


Determination  of  Canal  Cross-section. 


55 


is  to  be  lined  with  material  which  can  be  readily  shaped  into  this 
form.  If  the  canal  is  to  be  lined  with  stone  masonry  it  is  fre- 
quently more  advantageous  to  make  the  face  perpendicular  and 
to  place  the  batter  of  the  wall  at  the  back.  Where  the  canal  is  cut 
from  stone  or  shales  which  will  not  readily  disintegrate  in  contact 
with  the  water,  a  slope  of  90°  to  40°  may  be  sometimes  used. 
Quite  steep  slopes  can  also  be  used  with  dry  masonry  walls.  In 
material  which  can  be  handled  with  pick  and  shovel,  slopes  may  be 
used  from  I  to  1.25  to  I  to  1.50.  With  artificial  banks  of  dirt  and 
gravel  a  less  slope  angle  is  necessary  and  the  slope  must  frequently 
be  made  as  low  as  one  to  two. 

Table  VI,  which  is  taken  partially  from  "Uber  Wasserkraft  und 
Wasser  Versorgungsanlagen,"  by  Ferdinand  Schlotthauer,  is  of 
considerable  value  in  determining  the  most  advantageous  cross- 
section  in  various  sections  which  may  be  adopted  in  the  construc- 
tion of  a  canal.  As  seen  in  the  discussion  above,  the  most  advan- 
tageous cross-section,  other  things  being  equal,  is  that  in  which  the 


r  \  . 

A 

Fig.  24. 

wetted  perimeter  is  a  minimum  or  the  hydraulic  radius  is  a  maxi- 
mum. The  following  general  discussion  of  the  relations  is  based 
on  Fig.  24.  From  this  figure  it  will  be  seen  that 

(16)  a  =  bd  +  d2cotor 

(17)  p  =  b  -f  2d  cosec  a 
The  transposition  of  (i/)  gives 

^18)  b  ==  p  —  2d  cosec  a 

Substituting  (18)  in  (16) 

(19)  a  =  dp  —  2d2  coseca  -f-  d2cotor 

The  above  equation  now  contains  the  area,  depth,  wetted  peri- 
meter and  functions  of  the  slope  angle,  in  this  case  a  constant. 
The  conditions  of  maximum  efficiency  of  a  canal  section  require 


56  Hydraulics. 

that  the  wetted  perimeter  be  a  minimum  or  what  amounts  to  the 
same  thing  with  a  given  wetted  perimeter  the  area  a  must  become 
a  maximum.  The  value  of  d  which  makes  a  the  maximum  is  de- 


termined by  putting  -—       =  o 


(20)  =  p  _  4d  cosec  a  +  2d  cota 

(21)  .      0  =  p  —  4d  cosec  a  +  2d  cota 

~"  4  coseca  —  2  cota 
Substituting  for  p  its  value  in  (17) 

b  4-  2d  cosec  a 


(23)  d  = 


4  cosec  a  —  2  cota 
Equation  (16)  transposed  reads 

(24)  b  =  a-dd2c0ta 

Substituting  this  value  in  (23)  we  have 

-  --  d  coto:  -f-  2d  cosec  a 


4  cosec  a  —  2  cot  a: 
Clearing: 

(26)  4d2cosec  a  —  2d2cota  =  a  —  d~cota  -f  2d2coseca 
Transposing: 

(27)  d2  =  -  -  -  -  - 

2coseca  —  cota 

Transforming  trigonometric  functions 


(28)  d2  =     2 

-: cos  a  cosec  a. 

gin  a 


(29)  =     2  —  sin  a  cos  a  cosec  a 

sin  a 

(30) 


2  —  cos  a: 
Finally: 


(31)  d  = 


a  sm  a 


2  —  cos  a 
Equation  (24)  may  be  written 

(32)  b  =  -| dcoto- 

Table  VI  is  calculated  from  the  formulas 


(31)  d  =  J  a  Sln  a 

\2  —  cos  a 


Determination  of  Canal  Cross-section, 


W     2 


o 

1  S 


*1 


-C         s-l   0) 


II 

^s 


ft 
Q 


T*J    ft 


a 


I*    i«   U   I 


^  ^  ^   i 

GO  GO         CO 

CO         CO         CO         *O 


i*   l«   U   I 


cS        oS      I  03 


CO  CO  1C 
O3  CO  O 
00  CO  i> 


U    Ice    L 

CO        CO        (M 


los      ios      |« 

311 


IcS      -      I 


<M 


los  L,U  U  I  03  IcS 

^  ^'    ^  >.  V  ^ 

^  C^         C^1  CO  GO  CO 

i— I  CC          r-5  O  <— i  O 

Tf  GO         CD  1C  Tf  CO 


U      los 

S    8 


lea     Ics     loj     I 


5r»        <^> 
1C        O 

C5          O          r-i 


I     I     1 


Ij,  2 

So 
9) 

CO 


57 


58  Hydraulics. 

(32)  b  =  -| d  cot  a 

(33)  B  =  b  +  2dcoto: 

(34)  p  =  b+-^ 

sin  a 

In  the  above,  a=cross-section  area;  d=depth  of  water  in  channel; 
b— bottom  width  ;  B=width  at  water  level ;  p=wetted  perimeter ; 

c=the  length  of  slope  which  is  equal  to 


sin  a: 

In  Table  VI  the  relation  of  these  functions,  for  the  slopes  ordi- 
narily used  in  practice  have  been  calculated  as  well  as  for  the  semi- 
circular section.  The  use  of  the  table  may  be  illustrated  as  fol- 
lows :  The  quantity  of  water  which  it  is  desired  to  deliver  is  de- 
termined by  the  conditions  of  the  problem  or  by  measurement.  The 
velocity  to  be  maintained  in  the  channel  is  determined  by  the  ex- 
isting slope,  the  nature  of  material  encountered,  or  the  friction 
head  which  it  is  found  desirable  to  maintain.  The  area  of  the 
cross-section  required  to  carry  the  quantity  q  with  velocity  v  is 
a=-^-  After  the  slope  angle  has  been  selected,  for  the  material  in 
which  the  channel  is  to  be  constructed,  the  corresponding  values 
may  be  taken  out  of  the  table  from  their  respective  columns  and 
multiplied  by  the  square  root  of  a.  The  result  thus  obtained  gives 
the  desired  dimensions.  If,  for  example,  we  desire  to  carry  100 
cu.  ft.  of  water  per  second  in  a  canal  at  a  velocity  of  2~  1/2  ft.  per 
second  at  which  velocity  small  pebbles  are  unaffected,  and  with  a 
side  slope  of  1.5  to  I,  which  is  suitable  for  loose  earth,  has  been 
decided  upon,  the  required  area  of  cross-section  will  be  100/2.5 
=40  sq.  ft.  The  square  root  of  40  is  6.33.  The  required  dimensions 
of  canal  as  taken  from  the  table  are 

Depth  d=  689  x  6.33=4.36  ft. 

Bottom  width  b— 418  x  6.33=2.65  ft. 

Top  width  6=2.485  x  6.33=15.73  ft.  and 

The  wetted  perimeter  p=2.9O4  x  6.33=18.38  ft. 
Computation  of  the  area  from  the  above  dimensions  gives  40  sq.  ft. 
Hence  the  work  has  been  checked. 

42.  The  Back  Water  Curve. — One  of  the  problems  which  be- 
comes very  important  in  many  water  power  installations  is  the 
effect  on  the  elevations  of  the  stream  produced  by  the  erection  of 
a  dam  or  other  obstruction  therein.  The  back  water  curve  can  best 
be  determined  by  the  use  of  the  simple  formula  of  flow,  equa- 
tion (13). 


Flow  of  Water  in  Pipes.  50 

(13)  v  =  Cv/riT 

From  this,  as  shown  in  equation  (15) 

(15)  q*  =  v'a*  =  2f5j!l» 

From  this  equation  can  be  derived 

*»>••  ".  =  ££=£  Xi 

With  L  constant,  h3  :  h'3  ::-£-  :  -£-,  therefore 

3          3 


That  is  to  say,  with  the  quantity  of  water  and  length  of  section 
constant,  if  the  coefficient  remains  constant  the  head  due  to  any 
obstruction  will  vary  in  accordance  with  equation  (36). 

Where  the  water  is  greatly  deepened  in  proportion  to  its  orig- 
inal depth  the  value  of  c  will  not  remain  constant  but  will  vary. 
Where  such  is  the  case  and  where  q2!  is  constant,  under  which 
condition 

h3  n'a3  p2  ha2  rpz 

/Q7\  -L.t  v/      *^ 

W'J  n   3    —        ^/3^          A    -7T    —    „  ,  «   „ ,   „ ,  o 


The  difficulties  in  the  determination  of  the  value  of  c  are,  of 
course,  obvious,  but  it  is  believed  that  the  back  water  curve  can 
be  closely  calculated  by  this  simple  formula  in  which  the  new 
value  of  c  is  the  only  factor  to  be  estimated,  and  where  the  other 
elements  of  the  problem  can  be  determined  by  actual  measure- 
ments. In  using  this  formula  the  original  value  of  c  under  exist- 
ing condition  of  flow  can  be  determined  by  calculation  based  on 
actual  observation  of  flow  under  different  conditions  of  water  and 
the  conditions  of  the  channel  under  the  new  regimen  can  be 
closely  estimated.  New  values  of  c  can  be  very  closely  estimated 
on  the  basis  of  the  values  known  to  exist  under  other  similar  cir- 
cumstances. This  method  will  permit  of  a  more  practical  solution 
of  the  problem  than  by  the  use  of  formulas  based  on  entirely  the- 
oretical consideration  of  conditions  which  can  never  be  approxi- 
mated in  practice. 

43.  Flow  of  Water  in  Pipes. — Mathematical  expressions  for  the 
flow  of  water  in  pipes  may  be  derived  from  either  of  the  funda- 
mental hydraulic  formulas 

v  =  CI/TS~  or  v  =  c-/2gh, 
Starting  with  the  former  equation,  in  the  case  of  a  pipe  flowing 


60  Hydraulics. 

full  the  hydraulic  radius  r—  -  -where  d  is  the  diameter  of  the  pipe 
and  for  s  we  may  substitute  -^       We  then  have 
(38)  '= 


In  a  pipe  of  unit  length  and  unit  diameter  without  friction  the 
flow  would  be  expressed  by  the  formula 

v3 
v  =  i/2gh   or  h  =  -JT— 

To  modify  this  for  friction  a  friction  factor  f  is  introduced  and  the' 
equation  then  reads  : 


The  friction  varies .  directly  as  the  length  and  is  assumed  to  vary 
inversely  as  the  diameter.  Hence,  for  any  pipe  of  length  1  and 
diameter  d  the  complete  equation  is : 

(39)  h3  =  f  JL  -Xl  or  v  : 

Placing  (38)  and  (39)  equal  it  will  be  found  that 

16.04 

iso  that  the  equations  can  be  made  equivalent  by  the  proper  modi- 
fications of  friction  factors.  An  extensively  used  formula  for  the 
determination  of  c  in  equation  (38)  is  that  of  Darcy.  It  reads  : 

(40)  C  =  7^  =^= 

For  new  pipe  a  =  .00007726  and  ft  —  .00009647. 
For  old  pipe  a  =  .0001543  and  ft  =  .00001291. 

These  coefficients  were  determined  from  experiments  on  small 
pipes  and  therefore  in  the  case  of  large  pipes  with  high  velocities 
the  velocities  computed  by  this  formula  are  too  small. 

Various  modifications  of  the  Chezy  formula,  having  the  general 
form 

(41)  v  =  crn  sm 

have  been  proposed  or  derived  from  experiments.  Lampes  and 
Flamant's  are  the  best  known  of  this  type.  Lampes  reads 

(42)  V  =  77.68dO.694    S0.555 

and  Flamant's 

(43)  v  =  cd*  s* 

in  which  c— 76.28  for  old  cast  iron  pipe  and  86.3  for  new  pipe. 


Flow  of  Water  in  Pipes. 

LOSS     OF     HEAD     IN     FEET     PER     100     FEET 


61 


62 


Hydraulics. 


The  value  of  c  in  the  formula  v=c\/rs  may  vary  from  75  to  150- 
for  large  cast  iron  pipe.  For  riveted  steel  pipe  the  coefficient  varies 
but  little  with  velocity  and  diameter  and  at  ordinary  velocities 
ranges  from  100  to  115.  A.  L.  Adams  gives  values  of  c  for  wood 
stave  pipe  ranging  from  100  to  170.  Experiments  on  the  Ogden 
pipe  line  showed  average  values  of  about  120. 

An  examination  of  the  various  formulas  proposed  for  calculating 
the  flow  of  water  in  pipes  will  show  a  very  wide  range  of  results 
For  example,  for  calculating  the  head  lost  in  a  four-foot  new  cast 
iron  pipe,  some  of  the  principal  formulas  offered  and  the  graphical 
solution  of  the  same  are  shown  by  Fig.  25.  From  these  results  it 
will  be  seen  that  the  data  from  which  the  formulas  were  derived 
are  evidently  obtained  under  widely  varying  conditions  and  that 
in  the  relation  of  such  formulas  for  use  on  important  work,  they 
must  be  chosen  after  a  careful  consideration  of  all  the  elements  of 
the  problem,  and  that  it  is  usually  much  better,  when  possible,  to 
utilize  the  original  data  and  observation  along  similar  lines  when 
such  can  be  obtained,  and  derive  the  formula  to  be  used  instead  of 
accepting  one  whose  basis  may  be  obscure  or  unknown. 

In  construction  where  pipes  are  short  and  comparatively  unim- 
portant, a  formula  may  be  selected'  which  seems  to  agree  with  the 


ASPHALT       COATED 
CAST       IRON       PIPE 
BY   TUTTON'S   FORMULA 
s 


0.00" — 


6.0 


Fig.  26. 


Flow  of  Water  in  Pipes. 


LAP-RIVETED  i 

BY     TUTTON'S    FORMULA  * 


Fig.  27. 


0.15 
0.14 
0.13 
0.12 
0.11 
0.10 
0.09 
O.OB 
0.07 
006 
O.OS 
0.04 
0.03 
0.02 
0.01 
0.00 

WOOD-STAVE       PIPE 
BY     TUTTONS     FORMULA 
V  =IS5R  6B  S  b' 

4 

/ 

/ 

1.4 
1.3 
1.2 
I.I 
1.0 
0.9 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
O.I 

o.o. 

? 

// 

/ 

/ 

v 

/ 

/ 

x 

/ 

/ 

/ 

X 

fr 

^ 

X 

^ 

^ 

- 

y 

/ 

f 

X 

X 

_ 

£/ 

x' 

x 

& 

':> 

^ 

X 

^ 

•^ 

x 

Xs 

S 

f 

-X* 

<"** 

. 

X 

^ 

Ix 

'. 

^ 

,.x 

^' 

x 

/I  x 

/ 

r.. 

i» 

^•< 

X 

r— 

i 

-^r"» 

Lx 

^ 

^ 

^ 

;:; 

^ 



^ 

5 

•^Z- 

.  —  •  —  • 

1 

0 

2.0 

3.0 

4.0                                    SO                                  6.C 

VELOCITY      IN      FEET      PER      SECOND 

Fig.  28. 


64  Hydraulics. 

elements  of  the  problem.  The  formulas  offered  by  Tutton  seem 
to  agree  well  with  the  actual  results  of  experiments  and  several 
diagrams  based  thereon  are  shown  in  the  following  pages.  In  two 
of  these  diagrams  (Figs.  26  and  27)  the  limiting  values  are  shown 
and  the  results  obtained  from  any  pipe  of  the  character  represented 
therein  should  lie  between  these  limits  depending  on  its  condition. 
44.  The  Flow  of  Water  Through  Orifices. — It  is  found  that 
water  flowing  through  an  orifice  in  the  side  of  a  vessel  acquires 
a  velocity  practically  equal  to  that  which  would  be  acquired  by  a 
falling  body  in  passing  through  a  space  equal  to  the  head  above 
the  center  of  the  opening,  i.  e., 

(44)  v=  i/2gh    =  8.025/E 

in  which 

v=velocity  of  spouting  jet. 
g=acceleration  of  gravity=32.2. 
h=head  on  opening. 

The  discharge  through  the  opening  would  therefore  be  (45)  q= 
va=aV2gh  or  practically  (46)  q=ca\/2gh  where  c  is  a  coefficient 
varying  with  the  size  and  shape  of  the  orifice  and  with  various 
other  factors. 

A  more  accurate  determination  of  the  theory  of  flow  through  a 
given  orifice  is  derived  as  follows: 

If  a  thin  opening  is  considered  at  a  depth  y  be- 
low the  surface  the  discharge  through  the  ele- 
mentary section  Idy  would  be 


I  1 


(47)  dq  =  Idy1/2gy 

Integrating  this   equation   between   the   limits 
2  and  hi  we  obtain  the  following: 
Fig.  29. 

(48)  q  =  |l(ha*  —  h,^)v/2g~    or  practically 

(49)  q  =  mfll/2^(hj-h1f) 

m  being  the  coefficient  of  practical  modification  due  to  condition 
of  the  orifice. 

45.  Flow  Over  Weirs. — In  a  weir  h1=o.     Hence  equation   (49) 
becomes 

(50)  q  =  m  (Dl/gg  h* 

in  which  h  is  the  head  on  the  crest  of  the  weir.     That  is,  the  ver- 
tical distance  from  the  water  level  above  to  the  crest  of  the  weir. 


Flow  Over  Weirs. 


For  practical  use  the  coefficient  m  together  with  the  constants 


~  and  2g  are  combined  as  follows: 

o 


c  =  m  §i/2g  =  M  !/2g   and  equation  (50)  becomes 


(51) 


=  c 


The  value  of  m  and  consequently  of  c  varies  with  the  shape  of 
the  weir  and  with  other  factors  and  must  be  determined  experi- 
mentally. This  has  been  done  with  weirs  of  many  forms,  both  by 
Bazin  in  France  and  by  Rafter  and  Williams  at  the  Cornell  hydrau- 
lic laboratory.  The  results  of  these  experimental  determinations 
are  given  by  Figs.  30  to  34,  .inclusive.  These  figures  are  reduced 
directly  from  the  diagrams  of  Mr.  Rafter  in  the  Report  of  the 
Board  of  Engineers  of  Deep  Waterways,  1900. 

In  practice  many  weir  formulas  are  in  use,  based  on  various  ex- 
periments and  observations.  The  formula  of  Francis',  equation 
(52),  is  probably  the  best  known  in  this  country.  It  is  best  adapted 
to  long,  sharp  crested  weirs  without  end  contractions. 


(52) 


q  =  3.32  111* 


oo 


Head  on  Crest  of  Weir  in 


Fig.  30. — Weir  Coefficients  for  Weirs  of  Various  Shapes. 


66 


Hydraulics. 


ad  on  Crest  of  Weir  in  Peer 


ZO  3.O  4.0 

Head  on  Crest  of  Weir  in  Feet 


Fig.  31. — Weir  Coefficients  for  Weirs  of  Various  shapes. 


Flow  Over  Weirs. 


Head  on  Crest  of  Weir  in  feet 

9n 10  4 


Head  on  Crest  of  Weir  in  Feet 


Fig.  32. — Weir  Coefficients  for  Weirs  of  Various  Shapes. 


Bazin,  Series 

Flat  crested  V 

3M.      (e.56  Feet)  wic 


Ftefey  and  Stearns'  Experiments  E 
not  crested 


MuHln's  Formuk 
Fiat  crested  w» 
Width  of  Crest, 


3.O          40         50          60          7.O         SO         9O         IO.O         HO          120         !3O 

Discharge  in  Cubic  Feet  per  second 

Figu 


Francis'  Formula  for 
Merrimack  Dam. 


rancfs'  Formula. 
Sharp  crested  Weir. 

Muttirva  Formula, 
"Sharp  crested  Wefr 


Bazin's  Formula  fbr  a 
High  sharp  c res-ted  Weir 


Feet 


U.S.BOARD  OF  ENGINEERS  ON  DEEP  WATERWAYS 
WATER  SUPPLY  DIVISION. 

Dmparative  Discharqe  over  Weirs,  by  different  Formulae, 
For  a    Single   Foot  of  Crest. 

Barirrs  Formula,  Q-mLHVSqR 


Crest,  measured  from  trie 
of  sf  fi  Water,  in  feet. 

of  Discharge,  derived  by 
t  fbr  «ach  Form  of  Weir  ' 
Francis'  Formula  fbr  a  Sharp  Cnesfea  Weir. 


Formufq  fbr  Oam  on  tfie  Mern'mac 
f?iver,  at  Lawrence,  Mass 
Q«  3.01206  LH'» 

FrizeilS  Formula  fora  Flat  Crested  weir 

Q-309LH* 
Muiiin's  Formula,  used  by  Cast  Indian  Engineers 

Q-S.SSLCH^ 

For  a  Sharp  Crest-eo  Weir 


>Q654-O.OIH 
For  a  riot  crested 


To  accompany  Report  on  Special 
Water  Supply  Investigation 


'«o      TTO       155       lao" 5o5     5rS      555 eio     84-o      §55      2&o      ?r 


one  linear  Foot  of  Crest. 


.^-P-AK 


7o 


Hydraulics. 


Head  on  Crest  of  Weir  in  Feet 


00 


Head  on  Crest  of  Weir  in  Feet. 


Fig.  33.— Weir  Coefficients  for  Weirs  of  Various  Shapes. 


Flow  Over  Weirs. 


0 

Head  on  Crest 

19                               20 

of 

f- 

Weir  in  Feet  . 

45 

i 

^ 

^f 

:f 

a 

si 

;t4 

I 

s 

EE:: 

44 

Sf 

5 

^ 

i 

=1 

t 

N 

5  G  ~J  - 

J  

t: 

4* 

-T~ 

i 

- 

•  -ir* 

I 

f> 

T 

1 

M 

Mii 

ii 

e 

K 

TH- 

i: 

«s 

$z 

u 

10 

i. 

4- 

'^ 

z: 

- 

]f 

i 

n 
— 

H  ~  • 

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Fig.  34.— Weir  Coefficients  for  Weirs  of  Various  Shapes. 


To  accompany  Report  on  Specjai 
Water  Supply  Ir.v/esJiqation 


1899 


-   MS  BOARD  OF  ENGINEERS  ON  DEEP  WATERWAYS 

WATER  SUPPLY  DIVISION 
Diaaram  showing  over  Weirs  with 


Ser 


:t-x 


a  sharp  cresied  we,r 


•me- 


Discharge 


in  Cubic  Feet  per 


Sections  cf  experimental  Weirs. 

Direction  of  now 


M 656 


Series  No. 1 17 


162 


173. 


130. 


170 


Header 

Crest  of 
Vetr  in 

nisrhartge  over  Weir,  for  a  lenqrth  of  one  Foot,  in  Cubic  Feet  per  Second.(Approx.mate, 

Series  No  117 

168 

173 

135 

130. 

170 

Sharp  g«WMte- 

Off' 
0.5 

10 

IS 
2.0 
25 
30 
3.5 

098 
295 
555 
856 

teas 

1583 
MOO 
SA45 

6.0 
148 

420 
750 
II  35 

1568 
2040 
3545 

0.0       ' 
1.16 
958 
686 
1085 
15.40 
2038 
25.80 
31  53 

1.20 
370 
7.ZO 
11.45 
16.50 
82.04- 
28.15 
34.75 

i.se 

396 
7.6O 
I2.0O 
I7.OO 
SB.  56 
2660 
35.15 

1.20 
3.90 
7.6* 

IE05 
17  l« 
22.S5 
29.10 
3568 

1  10 
333 

eie 

942 
13.16 
17.30 
2I9O 
86.64 

1      1      1      I 

J          1          1         , 

I 

L  1 

1 

—  iss  —  196    ao.o  —  ?rb  —  sso  —  g3 
br  one  linear  Foot  of  Crest. 

o    afar    SB'O     gfio     870    auo    iiao     AO.O     *io    -NIU     ^^     ^*u    JWU     .,-- 

ire  36. 


74 


Hydraulics. 


A  number  of  different  tormtilas  for  the  flow  over  weirs  are  given 
on  Fig.  35  and  the  flow  as  calculated  by  these  formulas  is  shown 
on  the  diagram.  L  in  these  formulas  represents  the  length  of  the 
weir  crest  which. in  the  dimension  above  is  represented  by  1. 

Figure  26  shows  graphically  the  results  of  the  application  of  the 
value  of  c  as  given  on  Figs.  30  to  34  as  compared  with  Francis* 
formula. 

In  small  weirs  the  effect  of  end  contraction  and  of  the  velocity 
of  approach  becomes  important  and  corrections  to  the  formulas 
must  be  applied  in  order  to  allow  for  those  influences. 

If  n  =the  number  of  end  contractions  and  the  effect  of  each  is  to 
reduce  the  effective  length  of  the  weir  by  one-tenth  the  head  on  the 
weir,  equation  (51)  will  become 


(53) 


q  =  c  (1  -  n 


* 


The  effect  of  the  velocity  of  approach  is  to  reduce  the  head  on 
the  weir  by  the  velocity  head.  This  reduction  is  given  by  the 
formula : 

(54)  ht==lJF 

in  which  v'=velocity  of  approach  and  h'=velocity  head. 

TABLE  VII. 

Coefficient  of  discharge  C  for  use  with  Hamilton  Smith,  Jr.' 's  formula  (56}  for 
flow  of  water  over  sharp  crested  weirs  having  full  contraction. 
1  =  length  of  weir. 


Effective 
head  =h 

.66 

1(?) 

0 

2.6 

3 

4 

5 

7 

10 

15 

19 

.1 
.15 
.2 
.25 
.3 
.4 
.5 
.6 
.7 
g 

.632 
.619 
.611 
.605 
.601 
.595 
.590 
.587 
.585 

.639 
.625 
.618 
.612 
.608 
.601 
.596 
.593 
.590 

.646 
.634 
.626 
.621 
.616 
.609 
.605 
.601 
.598 
595 

.650 
.637 
.629 
.623 
.618 
.612 
.607 
.604 
.601 
598 

.052 
.638 
.630 
.624 
.619 
.613 
.608 
.605 
.603 
600 

.053 
.639 
.631 
.625 
.621 
.614 
.610 
.607 
.604 
602 

.653 
.640 
.631 
.626 
.621 
.615 
.611 
.608 
.606 
604 

.654 
.640 
.632 
.627 
.623 
.617 
.613 
.611 
.609 
.607 

.655 
.641 
.633 
.628 
.624 
.618 
.615 
.613 
.612 
.611 

.655 
.642 
.634 
.628 
.624 
.619 
.616 
.614 
.613 
61? 

.656 
.642 
.634 
.629 
.625 
.620 
.617 
.615 
.614 
618 

9 

592 

596 

598 

600 

.603 

.606 

.609 

611 

61? 

1  0 

590 

593 

595 

.598 

.601 

.604 

.608 

610 

«11 

1  i 

.587 

.591 

.593 

.596 

.599 

.603 

.606 

609 

610 

1  2 

.585 

.589 

.591 

.594 

.597 

.601 

.605 

.608 

.610 

1  3 

.582 

.586 

.589 

.592 

.596 

.599 

.604 

.607 

.609 

1  4 

.580 

584 

587 

.590 

.594 

.598 

.602 

fiOfi 

609 

1  5 

582 

585 

.589 

.592 

.596 

.601 

605 

.608 

1  6 

.580 

.582 

.587 

.591 

.595 

.600 

.604 

.607 

1.7 

.594 

.599 

.603 

.607 

2.0 

i 

Literature. 


75 


To  allow  for  the  influence  of  velocity  of  approach  h'  must  be 
added  to  h  and  equation  (53)  becomes 

(55)  q  =  c(l-ni)(h  +  hi)* 

Experimental  results  at  the  hydraulic  laboratory  of  the  Uni- 
versity of  AVisconsin  show  that  for  small  sharp  crested  weirs,  with 
•end  contraction,  the  formula  (56)  of  Hamilton  Smith,  Jr.,  is  prac- 
tically correct: 

(56)  q  =  c  §  /2£  IbJ 
In  this  formula 

c=coefficient  of  discharge  (to  be  taken  from  Table  VII). 
h=observed  head  on  crest  (H)  plus  correction  due  to  velocity 
of  approach. 

Variations  in  the  forms  of  the  crest  of  weirs  and  in  the  arrange- 

o 

ment  of  sides  and  bottom  of  the  channel  of  approach  cause  con- 
siderable variation  in  their  discharging  capacity.  It  is  therefore 
apparent  that  unless  the  conditions  closely  agree  with  those  on 
which  experimental  data  is  available  that  the  error  of  calculation 
may  be  considerable. 

LITERATURE. 

REFERENCES    ON   GENERAL   HYDRAULICS. 

1.  Francis,  Jas.  B.     Lowell  Hydraulic  Experiments.     New  York.     D.  Van- 

Nostrand.     1883. 

2.  Fanning,  J.  T.     Hydraulic  and  Water  Supply  Engineering.     New  York. 

D.  Van  Nostrand  &  Co.     1886. 
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and  through  Open  Conduits  and  Pipes.     New  York.     Wiley  & 

Sons.     1886. 
3a.  Church,  Irving  P.     A  treatise  on  Hydraulics.     New  York,  Wiley  &  Sons, 

4.  Weisbach,   P.   J.     Hydraulics  and  Hydraulic  Motors.     Translated   by  A. 

Jay  Dubois.    New  York,  Wiley  &  Sons.     1891. 

5.  Carpenter,  L.  G.     Measurement  and  Division  of  Water.     Bulletin  No.  27, 

Colo.  Agri'c.  Expt.  Sta.,  Ft.  Collins,  Colo.     1894. 

6.  Bovey,  Henry  T.    A  Treatise  on  Hydraulics.    New  York.    Wiley  &  Sons. 

1895. 

7.  Merriman,    Mansfield.      Treatise   on    Hydraulics.     New   York.     Wiley    & 

Sons.     1903. 

8.  Hydrographic  Manual,  Water  Supply  and  Irrigation  Paper  No.  94.    U.  S. 

G.  S.     1904. 
•9.  Hoskins,  L.  M.     Hydraulics.     New  York,  Henry  Holt  &  Co.     1907. 

REFERENCES    ON   FLOW   OF   WATER    IN    CANALS. 

10.  Hill,  A.     Flow  o^  Water  in  Rivers  and  Canals.     Van.  Nost.  Eng.  Mag. 
Vol.  3,  p.  118.     1870. 


76  Hydraulics. 

11.  Gangtiillet,  E.     Uniform  Motion  in  Canals  and  Rivers.     Van.  Nost.  Eng. 

Mag.     Vol.  2,  p.  211.     1870. 

12.  Searles,  W.  H.     Slope  of  Water  Surface  in  the  Erie  Canal.     Trans.  Am. 

Soc.  C.  E.,  Vol.  G,  pp.  290-296.     1877. 

13.  Ellis,  Theo.  G.     Flow  of  Water.     Eng.  News,  Nov.   26,   1881,  Vol.   8,  pp. 

478-9. 

14.  Cunningham,  Allan.     General  Discussion  of  Flow  in  Canals.     Proc.  Inst. 

Civ.  Eng.     1882-83,  pp.  1-95. 

15.  Fteley,  A.  and  Stearns,  F.  P.     Flow  of  Water  in  Conduits.     Trans.  Am. 

Soc.  C.  E.,  Vol.  12   (1883),  p.  114. 

16.  Flynn,  P.  J.     Irrigation  Canals  and  Other  Irrigation  Works  and  Flow  of 

Water  in  Irrigation  Canals.     Denver,  Colo.     1892. 

17.  Adams,   A.    L.     Diagram    for   Calculating   Velocities,    Grades   and    Mean 

Radii  for  Flumes  and  Ditche«3.    Eng.  News,  Feb.  13,  1892,  p.  157. 

18.  Ganguillet,  E.  and  Kutter,  W.  R.     A  General  Formula  for  the  Uniform 

Flow  of  Water  in  Rivers  and  Other  Channels.  Trans,  by  Ru- 
dolph Herring  and  John  Trautwine.  New  York,  Wiley  &  Sons. 
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19.  Boussinesq,  H.     The  Gradual  Variations  in  the  Flow  of  Water  in  Chan- 

nels of  Large  Section.    Comptes  Rendus^    May  31,  1897. 

20.  Boussinesq,   J.     Experimental   Verification   of   the   Theory   of   Gradually 

Varied  Flow  in  Open  Channels.  Comptes  Rendus.  June  14,. 
1897. 

21.  The  New  Formula  of  Bazin.     Genie  Civil,  March  5,  1898. 

22.  A  New  Formula  by  Bazin  for  Computing  Flow  of  Water  in  Open  Chan- 

nels.    Eng.  News,  July  14,  1898. 

23.  Bazin's  New  Formula  for  Flow  in  Open  Channels.    Eng.  News,  1898,  Vol. 

2,  p.  26. 

24.  A  Study  of  a  New  Formula  for  Calculating  the  Discharge  of  Open  Chan- 

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25.  Determination  of  Flow  in  Rivers  and  Canals.   Zeitschr.  d  Oesterr.   Ing.  u> 

Arch.  Ver.,  Vol.  50,  pp.  533-534.     1898. 

26.  Swan,  Chas.  H.  and  Horton,  Theo.  M.     Hydraulic  Diagrams  for  the  Dis- 

charge of  Conduits1  and  Canals.  New  York,  Eng.  News  Pub. 
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27.  Crosthwaite,  Ponsby  Moore.     Two  Graphic  Methods  Applied  to  Hydraulic 

Calculations.     Engineering.     London.     July  15,  1898. 

28.  Concerning  the  Conception  of  a  Hydraulic  Moment  of  Conduit  Cross  Sec- 

tion. Zeitschr.  fur  Arch,  u  Ing.  Vol.  46,  1900.  Heft-Ausgabe. 
Col.  402-417. 

29.  Siedek,  Richard.     Studies  of  a  New  Formula  for  Estimating  the  Velocity 

of  Water  in  Brooks  and  Small  Channels.  Zeitschr.  d  Oesterr. 
Ing.  und  Arch.  Ver.  Vol.  55,  pp.  98-106.  1903. 

REFERENCES   ON   FLOW   OF   WATER   THROUGH   PIPES. 

30.  Francis,  Jas.  B.     Flow  Through  Pipes.     Trans.  Am.   Soc.   C.  E.  Vol.   2, 

ff          p.  45.     1872. 

31.  Daaach,  C.  G.    Flow  of  Water  in  Pipes  under  Pressure.    Trans.  Am.  Soc. 

C.  E.  Vol.  7,  p.  114.     1878. 

32.  Wehage,   H.     Friction   Resistance   in   Pipes.     Dingler's    Polytechnisches 

Journal,  1884,  p.  89. 


Literature.  77 


33.  Stearns,  P.  P.    Flow  of  Water  Through  a  48"  Pipe.    Trans.  Am.  Soc.  C. 

E.,  Vol.  14,  p.  1.     1885. 

34.  Mair,  J.  G.     Flow  Through  Pipes  at  Different  Temperatures.     Proc.  Inst. 

C.  E.  Vol.  84,  p.  424.     1886. 

35.  Duane,  James.    Effect  of  Tuberculation  on  Delivery  of  a  48"  Water  Main. 

Trana  Am.   Soc.  C.  E.  1893,  p.  26. 

36.  Tuttle,  Geo.  W.     Economic  Velocity  of  Transmission  of  Water  Through 

Pipes.    E'ng.  Rec.  Sept.  7,  1895. 

37.  Coffin,  Freeman  C.    The  Friction  in  Several  Pumping  Mains.    Eng.  News, 

Feb.  20,  1896. 

38.  Hawks,  A.  McL.     Flowage  Test  of  14"  Riveted  Steel  Main  at  New  West- 

minster, B.  C.     Eng.  News,  July  30,  1896. 

39.  Flow  of  Water  in  Wrought  and  Cast  Iron  Pipe.     Am.  Soc.  Mech.  Eng. 

Dec.  1897. 

40.  Herschel,  Clemens.     115  Experiments  on  the  Carrying  Capacity  of  Large 

Riveted  Metal  Conduits.    New  York.     John  Wiley  &  Sons.    1897. 

41.  Gould,  E.  Sherman.     The  Flow  of  Water  in  Pipes.     Am.  Mach.  Mar.  3, 

1898. 

42.  Hawks,  A.  McL.     Friction  Coefficient  for  Riveted  Steel  Pipes.    Proc.  Am. 

Soc.  C.  E.     Aug.  1899. 

43.  Fulton,  C.  H.    Flow  of  Water  in  Pipes.    Jour.  Ass'n  Eng.  Soc.    Oct.  1899. 

44.  Marx,  C.  D.,  Wing,  Chas.  B.,  and  Hoskins,  L.  M.     Experiments  on  the 

Flow  of  Water  in  the  Six  Foot  Steel  and  Wood  Pipe  Line  of 
the  Pioneer  Electric  Power  Company.  Proc.  Am.  Soc.  C.  E. 
Feb.,  1900;  April,  1900;  May,  1900. 

45.  Gregory,  John  H.     Diagram  Giving  Discharge  of  Pipes  by  Kutter's  For- 

mula.    E'ng.  Rec.  Nov.  3,  1900. 

46.  Formulas  for  Flow  in  Pipe.     Eng.  News,  1901.     Vol.  II,  pp.  98,  118,  332, 

476. 

47.  Noble,  T.  A.    Flow  of  Water  in  Wood  Pipes.    Trans.  Am.  Soc.  C.  E.   Vol. 

49,  1902. 

48.  Saph,  A.  V.  and  Schoder,  E.  W.   Experimental  Study  of  the  Resistance  of 

the  Flow  of  Water  in  Pipes.  Proc.  Am.  Soc.  C.  E.  May,  1903; 
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BEFEEENCES    ON    FLOW    OF   WATER    OVER    WEIRS. 

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Soc.  C.  E.     Vol.  12,  p.  1.     1883. 

50.  Francis,  J.  B.     Experiments  on  Submerged  Weirs.     Trans.  Am.  Soc.  C. 

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51.  Herschel,  Clemens.     Problem  of  the  Submerged  Weir.     Trans.  Am.  Soc. 

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52.  Investigations  on  the  Flow  over  Submerged  Weirs.     Zeitschr.  des  Ver. 

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53.  Hind,  R.  H.     Flow  over  Submerged  Dams.     Proc.  Inst.  C.  E.     Vol.  85,  p. 

307.     1886. 

54.  Kaberstroh,  Chas.  E.    Epxeriments  on  the  Flow  of  Water  Through  Large 

Gates  and  over  a  Wide  Crest.  Jour.  Ass'n  Eng.  Soc.  Jan.,  1890, 
p.  1. 


78  Hydraulics. 

55.  The  Flow  of  Water  over  Dams  and  Spillways.     Eng.  Rec.  June  2,  1900. 

56.  Flow  of  Water  over  Sharp  Crested  Weirs.    Annales  des  Fonts  et  Chaus- 

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Ver.     June  2,  1905. 

58.  Flynn,   A.    D.    and   Dyer,    C.   W.    D.      The    Cippoletti    Trapezoidal   Weir. 

Trans.  Am.  Soc.  C.  E.     July,  1894. 

59.  Werenskiold,  N.     Flow  of  Water  over  Rounded  Crest.     Eng.  News,  Jan. 

31,  1895.     Yj^^,  p.  75. 

60.  Frizzel,  J.  P.  and  HJ^^el,  Clemens.     Flow  over  Wide  Horizontal  Top 

Weirs.    Eng.  News,  1892,  Vol.  II,  pp.  290,  440,  446;  1895,  Vol.  I, 
p.  75. 

61.  Johnson,  T.  T.  and  Cooley,  E.  S.   New  Experimental  Data  for  Flow  over  a 

Broad  Crest  Dam.     Jour.  W.  Soc.  Engrs.     Jan.,  1896. 

62.  Wide  Crest  Weirs.     Bazin's  Formula.     Eng.  News,  1890.     Vol.  I,  p.  162. 

Vol.  II,  p.  577;  1896,  Vol.  I,  p.  26. 

63.  Experiments  on  Flow  over  Dams.    Eng.  News,  1900,  p.  207. 

64.  Rafter,  Geo.  W.     The  Flow  of  Water  over  Dams.     Proc.  Am.  Soc.  C.  E. 

Mar.,  1900. 

65.  Heyne  H.     Study  of  Hydraulic  Coefficients.     Zeitschr.  d  Oesterr  Ing.  u 

Arch.  Ver.    Dec.  5  1900. 

66.  Dery,  Victor  A.  E.  D.     Experiments  on  the  Measurement  of  Water  over 

Weirs.     Proc.  Inst.  C.  E.    Vol.  114,  p.  333.     1893. 

REFERENCES   ON   BACK   WATER   AND   INTERFERENCE. 

67.  Wood,  De  Volson.   Back  Water  in  Streams  as  Produced  by  Dams.   Trans. 

Am.  Soc.  C.  E.     Vol.  2,  pp.  255-261.     1873. 

68.  Hutton,  W.  R.    Back  Water  Caused  by  Contractions.     Trans.  Am.  Soc.  C. 

E.     Vol.  11,  pp.  212-240.     1882. 

69.  Gillmore,  Q.  A.     Obstruction  to  River  Discharge  by  Bridge  Piers.     Van. 

Nost.  Eng.  Mag.    Vol.  26,  p.  441.    1882. 

70.  Back  Water  from  Dams.     Eng.  Rec.     July  9,  1892. 

71.  Ferriday,  Robert.     Measurements  of  Back  Water.     Eng.  News,  1895,  Vol. 

II,  p.  28. 

72.  Frescolm.  S.  W.     Back  Water  Caused  by  Bridge  Piers  and  other  Obstruc- 

tions.   Jour.  Eng.  Soc.,  Lehigh  Univ.    Feb.,  1899. 

73.  The  Estimation  of  Damages  to  Power  Plants  from  Back  Water.     Eng. 

Rec.    April  26,  1902. 

74.  Harris,  E.  G.,  Taylor,  W.  D.,  Ladshaw,  Y.  E.     Back  Water  from  Dams. 

The  Effect  on   Meadow  Lands.     Eng.   News,   1902,  Vol.   II,   pp. 
142  and  316. 

75.  Tables  for  Computation  of  Swell  on  Open  Water  Courses.     Zeitschr.  fur 

Arch,  und  Ing.     Vol.  49,  Cols.  258-274.     1903. 

76.  Fliegner,    A.      A    New    Method    of    Computing   the    Back    Water    Curve. 

Schweizerische  Bauzeitung.     Aug.  22,  1903. 

77.  Tolman,  Breitslav.     The  Computation  of  Back  Water  Curves.     Oesterr. 

Wochenschr.  f  d  Oeffent  Baudienst.    July  1,  8,  1905. 


CHAPTER  IV. 

WATER  POWER. 

THE  STUDY  OF  THE  POWER  OF  A  STREAMlJ^FFECTED  BY  FLOW. 

46.  Source  of  Water  Power. — Water  power   depends   primarily 
on  the  flow  of  the  stream  that  is  being  considered  for  power  pur- 
poses, and  on  the  head  that  can  be  developed  and  utilized  at  the 
site  proposed  for  the  power  plant.     Both  head  and  flow  are  essen- 
tial for  the  development  of  water  power,  but  both  are  variable 
quantities  which  are  seldom  constant  for  two  consecutive  days  at 
any  point  in  any  stream.     The  variations  in  head  and  flow  radically 
affect  the  power  that  can  be  generated  by  a  plant  installed  folr 
power  purposes.     These  variations  also  greatly  affect  the  power 
that  can  be  economically  developed  from  a  stream  at  any  locality. 
The  accurate  determination  of  both  head  and  flow  therefore  be- 
comes very  important  in  considering  water  power  installations  and 
hence  should  receive  the  careful  consideration  of  the  engineer.     The 
neglect  of  a  proper  consideration  of  either  or  both  of  these  factors 
has  frequently  been  fatal  to  the  most  complete  success  of  water 
power  projects. 

47.  Factors  of  Stream  Flow. — The  quantity  of  water  flowing  in  a 
stream  at  any  time,  which  is  more  briefly  termed  "stream  flow" 
or  "run-off,"  depends  primarily  upon  the  rainfall.     It  is,  however, 
influenced  by  many  other  elements  and  conditions.    It  depends  not 
only  upon  the  total  quantity  of  the  yearly  rainfall  on  the  drainage 
area,   but   also   on   the   intensity   and   distribution   of   the   rainfall 
throughout  the  year.     In  addition  to  these  factors  the  geological 
structure  of  the  drainage  area,  the  topographical  features,  the  sur- 
face area  of  the  catchment  basin,  the  temperature,  the  barometric 
condition,  all  influence  and  modify  the  run-off.     Sufficient  data  is 
not  available  for  a  full  understanding  of  this  subject,  but  enough 
is  available  so  that  the  general  principles  involved  can  be  intelli- 
gently discussed  and  the  problems  considered  in  such  a  way  as  to 
give  a  fairly  satisfactory  basis  for  practical  work.     A.  knowledge 
of  the  importance  of  the  factors  above  mentioned  and  the  extent  to 
which  they  modify,  influence  or  control  stream  flow,  is  essential 


8o  Water  Power. 

to  a  broad  knowledge  of  water  power  engineering.     These  factors 
are  discussed  in  more  detail  in  chapters  VI,  VII  and  VIII. 

48.  Broad  Knowledge  of  Stream  Flow  Necessary. — The  flow  of 
a  stream  is  constantly  changing  and  any  single  measurement  of 
that  flow  will  not  furnish  sufficient  data  on  which  to  base  an  in- 
telligent estimate  of  the  extent  of  its  possible  or  even  probable 
economical  power  development.     A  knowledge  of  the  economical 
possibilities   of   such   development   must  be   based   upon   a   much 
broader  knowledge  of  the  variations  that  take  place  in  the  flow  of 
the  stream.     In   order  to  fully  appreciate  the   power  value   of  a 
stream,  the  character  and  extent  of  its  daily  fluctuations  must  be 
known  or  estimated.    Averages  for  the  year,  monthly  averages,  and 
estimates  of  average  power  have  been  ordinarily  taken  as  a  basis 
for  water  power  estimates,  but  they  are  more  or  less  misleading, 
unsatisfactory  and  uncertain  for  the  reason  that  such  averages  in- 
clude extremes,  the  maximum  of  which  are  often  unavailable  for 
water  power  purposes   without   more   extensive   pondage   than   is 
usually  practicable.     These  maximum  and  minimum  flows  which 
affect  the  power  of  a  stream  not  only  through  the  quantity  flowing 
but  also  through  the  head  as  well,  as  will  be  hereafter  discussed, 
are  of  the  utmost  importance  for  a  broad  consideration  of  water 
power.     So  also  is  a  knowledge  of  the  various  stages  of  flow  and 
the  length  of  time  that  each  will  prevail.    Such  knowledge  demands 
daily  observations  or  estimates  of  daily  flow  which  can  be  repre- 
sented in  graphical  form  by  the  hydrograph. 

49.  The  Hydrograph. — The  hydrograph,  constructed  for  the  study 
of  stream  flow  and  its  influence  on  water  power,  may  be  drawn  by 
representing  the  daily  flow  in  cubic  feet  per  second  at  the  point 
of  observation  by  the  ordinates  of  the  diagram  and  the  element  of 
time  by  the  abscissas.     (See  Fig.  37.)     The  result  is  a  graphical 
diagram  which  shows  the  character  and  extent  of  the  daily  fluctua- 
tions in  the  flow  of  a  stream  at  the  point  of  observation  during  the 
period  for  which  the  hydrograph  has  been  prepared. 

A  single  observation  of  the  flow  of  a  stream  represents  a  totally 
inadequate  and  unsatisfactory  criterion  for  water  power  consid- 
eration. By  reference  to  Fig.  37  it  will  be  seen  that,  if  the  dis- 
charge of  the  Wisconsin  River  at  Necedah  had  been  measured  only 
on  August  5,  1904,  the  conclusion  would  have  been  reached  that 
the  discharge  of  the  river  was  about  2,100  cubic  feet  per  second. 
If  the  measurement  had  been  taken  only  on  August  15,  1904,  the 
flow  would  have  been  determined  at  about  5,850  cubic  feet  per 
second,  or  almost  three  times  as  great  as  on  the  first  date.  The 


The  Hydrograph. 


81 


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82  Water  Power. 

difference  between  the  dates  might  be  even  greater,  and  no  single 
measurement  nor  any  series  of  rneasurements  for  a  single  week  or 
month  would  give  a  fair  criterion  from  which  the  normal  flow  of 
the  river  could  be  judged. 

The  hydrograph  of  the  daily  flow  of  a  river  for  a  single  year 
gives  a  knowledge  of  the  variation  in  flow  for  that  year  only, 
under  the  peculiar  conditions  of  the  rainfall,  the  evaporation,  and 
the  other  physical  factors  that  modify  the  same  and  that  obtain 
for  that  particular  year.  Such  information,  while  important,  is  not 
altogether  sufficient  for  the  purpose  of  a  thorough  understanding 
of  the  availability  of  the  stream  flow  for  power  purposes.  Observa- 
tions show  that  stream  flow  varies  greatly  from  year  to  year,  and, 
while,  with  a  careful  study  of  the  influences  of  the  various  factors 
on  stream  flow,  together  with  a  knowledge  of  the  past  variations 
in  such  factors,  the  hydrograph  for  a  single  year  may  give  a  fairly 
clear  knowledge  of  the  variations  to  be  expected  in  other  years 
where  conditions  differ  considerably,  still  it  is  desirable  that  the 
observations  be  extended  for  as  long  a  period  as  possible.  Such 
long  time  observations  may  remove  the  estimates  of  flow  entirely 
irom  the  domains  of  speculation  and  place  them  on  the  solid  ground 
of  observed  facts.  Hydrographs  of  a  river  that  cover  the  full  range 
of  conditions  of  rainfall,  temperature,  etc.,  which  are  liable  to  pre- 
vail on  its  drainage  area,. give  a  very  complete  knowledge  of  the 
flow  of  the  stream  for  the  purpose  of  the  consideration  of  water 
power. 

It  is  rare,  however,  that  observations  of  stream  flow  for  a  long 
term  of  years  are  available  at  the  immediate  site  of  a  proposed 
power  plant.  Such  observations  are  ordinarily  made  only  at  loca- 
tions where  power  has  been  developed  and  where  water  power  or 
similar  interests  have  been  centered  for  a  long  period  of  time.  Oc- 
casionally, however,  the  future  value  of  potential  powers  is  recog- 
nized and  appreciated,  and  local  observations  are  maintained  for  a 
series  of  years  by  interested  parties,  having  a  sufficient  knowledge 
of  the  subject  to  recognize  the  value  and  importance  of  such  in- 
formation. The  variation  of  flow  for  some  considerable  time  pre- 
vious to  construction  is  thus  available  upon  which  to  base  the  design. 

In  .considering  new  installations,  one  of  four  conditions  obtains : 

First :  Hydrographs  are  available  at  the  immediate  site  proposed. 

Second:  Hydrographs  are  available  at  some  other  point  on  the 
river  above  or  below  the  proposed  installation. 


The  Use  of  Local  Hydrographs.  83 

Third :  Hydrographs  are  not  available  on  the  river  in  question 
but  are  available  on  other  rivers  where  essentially  similar  condi- 
tions of  rainfall  and  stream  flow  prevail. 

Fourth :  No  hydrographs,  either  on  the  river  in  question  or  on 
other  rivers  of  a  similar  character  and  in  the  immediate  vicinity, 
are  available. 

50.  The  Use  of  Local  Hydrographs. — When  hydrographs,  con- 
structed from  observations  taken  at  the  immediate  site  of  the  pro- 
posed water  power  installation,  are  obtainable,  for  a  considerable 
number  of  years,  the  most  satisfactory  -character  of  information  is 
available  for  the  consideration  of  a  water  power  project.     Under 
such  conditions  the  engineer  is  not  obliged  to  consider  the  rela- 
tion of  rainfall  to  run-off  or  to  speculate  as  to  the  relative  value  of 
the  stream  in  question  compared  with  other  adjacent  streams,  or 
as  to  the  effects  of  the  physical  conditions  of  drainage  area,  evap- 
oration, temperature  and  other  factors  on  stream  flow.    The  actual 
daily  flow  of  the  stream   from   day  to   day,   perhaps  through  all 
ranges  of  rainfall,  temperature,  evaporation  and  other  physical  con- 
ditions, is  known  and  the  principal  points  which  must  be  consid- 
ered are :  First,  the  head  available ;  Second,  the  effects  of  the  varia- 
tions of  flow  on  the  variations  in  head ;  and  Third,  the  extent  to 
which  the  flow  can  be  economically  develo'ped  or  utilized.     Gen- 
erally, however,  even  where  local  hydrographs  are  available,  they 
are  not  sufficiently  extended  to  cover  all  the  variations  in  river  flow 
which  must  be  anticipated,  and  it  is  ordinarily  desirable  to  com- 
pare the  available  data  with  the  flow  at  other  points  on  the  stream 
in  question  or  with  other  streams  in  the  immediate  vicinity. 

51.  Use  of  Comparative  Hydrographs. — Hydrographs  taken  at 
other  points  on  the  same  river,  or  on  other  adjacent  rivers  where 
conditions  are  reasonably  similar,  are  of  great  value  in  considering 
the  local  stream  flow, — provided  all  modifying  conditions  are  under- 
stood and  carefully  considered.     Hydrographs  are  ordinarily  pre- 
pared to  show  the  cubic  feet  per  second  of  actual  flow  at  the 
point  at  which  observations  are  made.     If  the  observations   (and 
the  hydrographs  based  thereon)   made  at  some  other  point  on  a 
stream,  of  on  some  other  streams,  are  to  be  used  for  jthe  considera- 
tion of  the  flow  at  a  point  where  a  water  power  plant  is  to  be 
installed  or  considered,   the   relation   of  the   flows   at  the   several 
points  must  be  determined. 

As  a  basis  for  such  comparison  of  stream  flow,  it  may  be  as- 
sumed that  the  flow  per  unit  of  area  at  different  points  on  the  same 


Water  Power. 


Fig.  38. — Drainage  Area  of  Wisconsin  River  Above  Kilbourn,  Wis. 


Use  of  Comparative  Hydrographs.  85 

% 

stream,  or  at  points  on  different  streams  under  similar  circum- 
stances, is  essentially  the  same.  This  is  not  strictly  true,  or  per- 
haps it  may  be  more  truly  said  that  the  apparent  similarity  of  condi- 
tions is  only  approximate  and  hence  differences  in  results  must 
necessarily  follow.  For  a  satisfactory  consideration  of  the  subject 
of  comparative  hydrographs,  the  variations  from  this  assumption, 
as  discussed  in  another  chapter,  must  be  understood  and  appre- 
ciated. For  practical  purposes,  however,  the  assumption  is  often 
essentially  correct  and  forms  a  basis  for  an  intelligent  considera- 
tion of  stream  flow  where  local  hydrographs  are  not  available.  Fig. 
37  is  a  hydrograph  constructed  from  observations  made  on  the 
Wisconsin  River  at  Necedah,  Wisconsin,  by  the  U.  S.  Geological 
Survey  for  the  water  year,  1904,  and  shows  the  daily  rate  of  dis- 
charge of  the  Wisconsin  River  at  that  point  for  the  year  named. 
The  area  of  the  Wisconsin  River  (see  Fig.  38)  above  Necedah  is 
5,800  square  miles.  If,  therefore,  we  draw  a  horizontal  line  from 
the  point  representing  5,800  cubic  feet  per  second  on  the  discharge 
scale  (see  Fig.  37),  the  line  so  drawn  will  represent  a  discharge  at 
Necedah  of  one  cubic  foot  per  second  per  square  mile  of  drainage 
area,  and  a  similar  line  drawn  from  the  11,600  cubic  foot  point  on 
the  vertical  scale  will  represent  a  discharge  of  two  cubic  feet 
per  second  per  square  mile,  and  so  on.  These  lines  may  be  fairly 
regarded  not  only  as  indicating  the  flow  per  unit  of  area  of  the  - 
river  at  Necedah,  but  also  the  relative  flow  per  unit  of  area  of  the 
Wisconsin  River  at  points  not  greatly  distant  therefrom.  At  Kil- 
bourn,  (see  Fig.  38)  located  on  the  same  river  about  forty  miles 
below  Necedah,  the  flow  may  be  assumed  to  be  similar  and  pro- 
portionate to  the  flow  at  Necedah.  Above  Kilbourn  the  drainage 
area  is  7,900  square  miles,  and  with  similar  flow  the  discharge 
would  be  proportionately  greater.  The  fact  must  be  recognized, 
and  acknowledged,  that  the  hydrograph  is  strictly  applicable  only 
to  the  point  at  which  it  is  taken,  and  that  certain  errors  will  arise 
in  considering  its  application  to  other  points,  yet  observations  and 
comparisons  show  that,  while  such  errors  exist,  they  are  not  nearly 
so  important  as  the  errors  which  arise  from  the  consideration  of 
averages,  either  annually  or  monthly. 

Consider,  therefore,  on  this  basis  the  Necedah  hydrograph  as 
shown  in  Fig.  37.  On  this  diagram  a  flow  of  one  cubic  foot  per 
second  per  square  mile  at  Necedah,  representing  an  actual  flow  of 
5,800  cubic  feet  per  second  at  that  point,  would,  by  proportion, 
represent  a  flow  of  7,900  cubic  feet  per  second  at  Kilbourn  and, 


86 


Water  Power. 


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Reliability  of  Comparative  Hydrographs.  87 

with  a  suitable  change  in  scale,  the  diagram  may  be  redrawn  to  rep- 
resent the  flow  at  Kilbourn  as  shown  in  Fig.  39.  This  same  method 
can  be  applied  to  any  point  on  the  same  river  or  to  comparative 
points  on  different  rivers. 

52.  Reliability  of  Comparative  Hydrographs. — It  must  be  clearly 
understood  that  comparisons  as  above  described  hold  good  only 
as  the  conditions  are  essentially  similar  at  the  various  points  com- 
pared. 

Stream  flow  at  the  best  is  very  irregular  and  varies  greatly  from 
year  to  year.  The  actual  departure  from  the  truth  can  best  be 
understood  and  appreciated  from  an  actual  comparison  of  flows 
on  adjacent  drainage  areas  where  observations  have  actually  been 
made  for  a  term  of  years.  From  such  an  investigation,  which  can 
be  made  as  extended  as  desirable,  the  true  weight  to  be  given  to  the 
comparative  hydrograph  can  best  be  judged.  It  is  not  believed 
that  the  actual  variations  from  the  truth,  as  shown  by  carefully 
selected  comparative  hydrographs,  will  be  any  greater  than  the  flow 
variations  which  actually  take  place  from  a  drainage  area  from  year 
to  year  under  the  varying  conditions  of  rainfall  and  climate.  This 
method,  therefore,  is  believed  to  be  a  scientific  and  systematic  one 
for  the  consideration  and  discussion  of  probable  variations  in  stream 
flow  at  any  given  point,  if  its  limitations  and  the  modifying  in- 
fluences known  to  exist  on  different  drainage  areas  and  under 
different  geographical,  geological  and  meteorological  conditions  are 
knowrn  and  appreciated. 

53.  When  no   Hydrographs  are  Available. — In   a  new  country 
where  no  observations  are  available  either  on  the  drainage  area 
under  consideration  or  on  other  areas  adjacent  thereto,  the  study 
of  comparative  hydrographs  is  impossible  and  a  different  method 
of  consideration  must  be  used.    If  no  data  are  available,  time  must 
be  taken  to  acquire  a  reasonable  amount  of  local  information  which 
should  include  not  less  than  one  year's  observation.     In  addition 
to  such  observation  a  study  as  thorough  as  practicable  should  be 
made  of  the  geology,  topography,   and  other  physical   conditions 
that  prevail  on  the  water  shed.     Rainfall  data  is  commonly  avail- 
able for  a  much  greater  range  of  time  than  the  observations  of 
stream  flow.    The  relations  of  rainfall  to  run-off  are  hereafter  dis- 
cussed and  approximate  fixed  relations  are  shown  to  exist  between 
them.     From  such  relations,  and  from  a  single  year's  observations,, 
conclusions  may  be  drawn  as  to  the  probable  variations  from  the 
observed  flow  which  will  occur  during  the  years  where  the  rainfall 


Water  Power. 


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varies  greatly  from  that  of  the  year  during  which  observations  are 
available.  Such  conclusions  are  necessarily  unsatisfactory,  or  at 
least  much  less  satisfactory  than  conclusions  based  on  actual 
stream  flow.  The  consideration  of  the  best  information  available 
on  any  project  is  the  basis  on  which  the  engineer  should  always 
rest  his  conclusions,  and  all  relations  which  will  throw  light  "on  the 
actual  conditions  should  be  given  careful  attention.  If  a  water 
power  plant  must  be  immediately  constructed  upon  a  stream  con- 
cerning which  little  or  no  information  is  available,  then  the  risk  is- 
proportionately  greater,  and  safety  is  obtained  only  by  building 
in  such  a  conservative  manner  that  success  will  be  assured  for  the 
plant  installed  and  on  plans  that  will  permit  of  future  extensions 
should  the  conditions  that  afterward  develop  warrant  an  extension 
of  the  same. 

54.  The  Hydrograph  as  a  Power  Curve. — The  hydrography  by  a 
simple  change  in  the  vertical  scale  similar  to  that  already  consid- 
ered, may  also  be  made  to  show  graphically  the  variations  in  the 
power  of  the  stream.  If,  for  example,  at  Kilbourn,  a  constant  fall  of 
seventeen  feet  be  assumed,  then  a  flow  of  one  cubic  foot  per  second 
per  square  mile  represents  a  total  flow  of  7,900  cubic  feet  per  second, 
and  this  flow,  under  17  foot  head,  will  give  a  theoretical  hydraulic 
horse  power  as  follows: 

7900X17       1t.9A1 

±i..F.  =  J-TJ =  15251 

o.o 

Now  if  a  hydrograph  be  constructed  on  such  a  scale  that  the  line  of 
flow  of  one  cubic  foot  per  second  per  square  mile  will  also  repre- 
sent 15,261  horse  power,  the  result  will  be  a  power  hydrograph 
(see  Fig.  40),  which  represents  the  continuous  (24  hours  per  day) 
theoretical  power  of  the  river  under  the  conditions  named. 

On  account  of  losses  in  the  development  of  power  the  full  theoret- 
ical power  of  a  stream  cannot  be  developed,  and  hence  the  actual 
power  that  can  be  realized  is  always  less  than  the  theoretical  power 
of  the  stream.  If  it  is  desired  to  consider  the  actual  power  of  the 
stream  on  the  basis  of  developing  the  same  with  turbines  of  80 
per  cent  efficiency,  the  line  representing  the  flow  of  one  cubic  foot 
per  second  per  square  mile  will  represent  the  actual  horse  power 
to  an  amount  determined  as  follows: 

_  7900  X  17  X  .80  _    7900  X  17  _ 
8.8  TT~ 

A  hydrograph  platted  so  that  the  line  of  one  cubic  foot  per 
square  mile  will  represent  this  amount,  will  represent  the  actual 


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92  Water  Power. 

horse  power  of  the  river  at  Kilbourn  with  the  wheels  working  with 
the  efficiency  and  under  the  head  named.  Such  a  hydrograph  is 
shown  by  Fig.  41,  referred  to  by  the  left-hand  scale  (A).  Power, 
however,  is  not  always  used  continuously  for  twenty-four  hours. 
If  pondage  is  available  the  night  flow  may  be  stored  and  utilized 
during  the  day.  If  the  flow  of  twelve  hours  at  night  is  impounded 
and  used  during  the  day  under  the  seventeen  foot  head,  the  power 
will  be  double  that  shown  on  scale  A,  and  can  be  represented  by 
another  change  in  scale  as  shown  by  Fig.  41,  referred  to  scale  B. 
If  the  flow  for  the  fourteen  hours  of  night  is  stored  and  utilized  in 
the  ten  hours  of  day,  then  the  hydrograph  can  be  made  by  another 
change  in  scale  to  represent  the  ten  hours  power  as  shown  by 
Fig.  42. 

The  total  horse  power  hours  which  are  available  from  a  stream 
for  each  day  may  be  represented  (either  theoretically  or  actually) 
by  multiplying  the  scale  of  continuous  power  by  24.  The  actual 
horse  power  available  at  Kilbourn  under  the  conditions  named  is 
represented  by  scale  C  in  Fig.  41.  It  will  be  noted  that  by  pointing 
off  one  place  in  the  figures  of  scale  C,  Fig.  41,  the  hydrograph  will 
represent  the  same  condition  as  shown  in  Fig.  42. 


CHAPTER  V. 

WATER  POWER  (Continued.) 
THE  STUDY  OF  THE  POWER  OF  A  STREAM  AS  AFFECTED  BY  HEAD. 

55.  Variations  in  Head. — In  the  previous  chapter  the  graphical 
representation  of  stream  flow  has  been  considered.  A  method  for 
the  expression  of  the  power  resulting  from  the  fluctuations  of 
stream  flow  and  under  a  constant  head  has  also  been  shown.  Ex- 
perience shows,  however,  that  such  a  condition  seldom  if  ever 
occurs.  In  some  cases  where  the  available  head  is  a  very  large 
element  of  the  possible  power,  the  fluctuations  may  be  so  small 
as  to  be  of  little  or  no  importance.  In  many  other  cases  where  the 
available  heads  are  considerable,  the  importance  of  the  fluctuation 
in  head  is  comparatively  small,  under  which  condition  the  diagrams 
already  discussed  are  essentially  correct  and  are  satisfactory  for 
the  consideration  of  the  varying  power  of  the  stream.  In  power 
developments  under  the  low  heads  available  in  many  rivers,  the 
fluctuation  in  head  is  almost  or  quite  as  influential  on  the  con- 
tinuous power  that  may  be  economically  developed  from  a  stream 
as  the  minimum  flow  of  the  stream  itself. 

The  hydraulic  gradient  of  a  stream  varies  with  the  quantity  of 
water  flowing.  At  times  of  low  water  the  fall  available  in  almost 
every  portion  of  its  course  is  greater  than  is  necessary  to  assure 
the  flow  between  given  points  and  frequent  rapids  result  (see  R. 
R.  Fig.  43)  which  are  commonly  the  basis  for  water  power  develop- 


Flood      flow. 

Medium    Water 
Low     Water 
Stream     Bed- 


Fig.  43. — Hydraulic  Gradients  of  a  Stream  Under  Various  Conditions 

of  Flow. 


94 


Water  Power. 


ments.  As  the  flow  increases,  however,  a  higher  gradient  and 
greater  stream  section  is  necessary  in  order  to  pass  the  greater 
quantity  of  water,  and  the  rapids  and  small  falls  gradually  become 
obscured  (as  shown  by  the  medium  water  lines,  Fig.  43)  or  dis- 
appear entirely  under  the  larger  flows  (as  shown  by  the  higher 
water  line,  Fig.  43).  Water  power  dams  concentrate  the  fall  of  the 


Hood    Mow 
Medium  Wafer 
Low  Water. 
Stream    Bed. 


Fig.  44. — Hydraulic  Gradients  of  the  Same  Stream  After  the  Construction  of 
Dam  and  Under  Various  Conditions  of  Flow. 

river  that  is  unnecessary  to  produce  flow  during  conditions  of  low 
and  moderate  water  (as  shown  in  Fig.  44),  and  when  the  gradient 
of  the  water  surface  and  the  cross  section  of  the  stream  are  in- 
creased to  accommodate  the  larger  flow,  the  fall  at  such  dams  is 
frequently  greatly  reduced  (as  shown  by  the  medium  water  line  in 
Fig.  44)  or,  during  high  water,  the  fall  is  largely  or  completely  de- 
stroyed (as  shown  by  the  high  water  lines  in  the  Figure),  or  at 
least  is  so  reduced  as  to  be  of  little  or  no  avail  under  practical  water 
power  conditions. 

The  cross  section  of  the  river  bed,  its  physical  character  and 
longitudinal  slope,  are  the  factors  which  determine  the  hydraulic 
gradient  of  a  stream  under  different  flows.  They  are  so  variable 
in  character  and  their  detail  condition  is  so  difficult  of  determina- 
tion that  sufficient  knowledge  is  seldom  available,  except  possibly 
in  the  case  of  some  artificial  channels,  to  determine,  with  reason- 
able accuracy,  the  change  of  the  surface  gradient  and  cross  section 
of  the  water  under  various  conditions  of  flow.  Where  a  power  plant 
is  to  be  installed,  it  is  important  to  ascertain  the  relation  of  flow 
to  head  in  order  that  the  available  power  may  be  accurately  deter- 
mined. Where  a  river  is  in  such  condition  as  to  make  the  de- 
termination of  a  discharge  rating  curve  possible,  either  by  direct 
river  measurement  at  the  point  in  question  or  by  a  comparison  with 
the  flow  over  weirs  at  some  other  point,  such  determination  should 
be  carefully  made,  as  such  knowledge  is  of  the  utmost  importance 
in  considering  the  problem  of  continuous  power. 


The  Rating  Curve. 


95 


56.  The  Rating  or  Discharge  Curve. — The  rating  curve,  which 
will  be  discussed  in  some  detail  in  a  later  chapter,  is  a  hydrograph 
that  represents  the  relation  of  the  elevation  of  the  water  surface  in  a 
channel  to  the  quantity  of  water  passing  a  given  cross  section.  The 
form  of  this  curve  varies  with  the  various  conditions  of  the  cross 
section  both  at  the  immediate  point  and  for  a  considerable  distance 
above  and  below  the  location  considered  and  can  usually  be  de- 
termined only  by  detail  observations.  The  rating  curve  is  a  uni- 
form curve  only  for  channels  in  which  no  radical  change  in  form  of 
cross  section  occurs  with  the  increase  of  flow.  (See  A  Fig.  45.)  If, 
on  account  of  overflow  conditions,  or  sudden  enlargements  of  the 
cross  section,  that  cross  section  varies  radically  in  form  at  a  given 
height,  then  at  this  elevation  a  radical  change  in  the  slope  of  the 
rating  curve  is  likely  to  occur.  (See  B  and  C  Fig.  45.) 


B 


Fig.  45. — The  Influence  of  the  Stream  Cross  Section  on  the  Rating  Curve. 

Any  change  in  the  bed  of  the  stream  may,  and  frequently  does, 
modify  to  a  considerable  extent  the  rating  curve,  which  must  be 
expected  to  vary  under  such  conditions  to  an  extent  that  depends 
on  the  variations  that  take  place  in  the  cross  section  and  elevation 
of  the  stream  bed.  Such  variations,  however,  are  not,  as  a  rule,  of 
great  magnitude  and  consequently  will  not  usually  affect  the  head 
materially  at  a  given  point. 


96 


Water  Power. 


In  Fig.  46,  which  shows  the  rating  curve  of  the  Wisconsin  River 
at  Necedah,  Wis.,  as  determined  at  different  times  during  the  years 
1903  and  1904,  an  extreme  change  of  head  of  about  six  inches  will 
be  noted  for  ordinary  flows.  When  the  change  in  head  is  of  suf- 


fcJC 


£ 


Sfcrf 


*• 


'<£- 


EC 


3  , 130* 


Discharge  in  Cu.  Ft.  Per  Second. 

Fig.  46. — Rating  Curves,  Wisconsin  River  at  Necedah,  Wis.,  Showing  Changes 
in  Head  Due  to  Changes  in  Cross  Section, 

ficient  importance  to  warrant  the  expense,  the  river  channel  may  be 
so  dredged  out  as  to  restore  the  original  head  when  the  reduction 
in  head  is  occasioned  by  the  filling  of  the  section. 

57.  The  Tail  Water  Curve. — It  will  be  readily  seen  that  while  the 
rating  curve  shows  the   relation  between   stream   flow   and   river 
height  prior  to  the  construction  of  a  dam,  it  will  still  represent  the 
condition  of  flow  below  the  dam  after  construction  is  completed. 
The  water  flowing  over  the  dam  will  create  a  disturbed  condition 
immediately  below.    If  the  velocity  of  the  flow  is  partially  checked 
or  entirely  destroyed,  a  heading-up  of  the  water  may  result  below 
the  dam  sufficient  to  give  the  velocity  required  to  produce  the  flow 
in  the  river  below,  but  it  will  soon  reach  a  normal  condition  similar 
to  that  which  existed  previous  to  the  construction  of  the  dam. 

58.  The  Head  Water  Curve. — In  Chapter  III  is  shown  (see  Figs. 
35  and  36)  the  discharge  curves  over  weirs  of  various  forms  and  the 
formulas  representing  them  are  also  quite  fully  discussed.     From 


The  Graphic  Representation  of  Head. 


97 


these  formulas  or  diagrams  a  discharge  curve  can  be  readily  cal- 
culated, with  reasonable  exactness,  for  a  dam  with  a  certain  form 
and  length  of  crest.  Such  a  curve  will  show  the  height  of  the  head 
waters  above  the  dam  and  under  any  assumed  conditions  of  flow. 
From  the  rating  curve  of  the  river  at  the  point  considered,  and  the 
discharge  curve  of  the  weir  proposed,  the  relative  positions  of  head 
and  tail  waters  under  varying  conditions  of  discharge  can  be  readily 
and  accurately  determined,  and  if  a  weir  is  to  be  built  to  a  certain 
fixed  height,  it  will  be  seen  that  the  head  under  any  given  conditions 
of  flow  may  be  thus  determined. 

59.  Graphic  Representation  of  Head. — Fig.  47  shows  the  rating 
curve  of  the  Wisconsin  River  (see  lower  curve  marked  "Tail  Water 


DISCHARGE    IN    CUBIC    FEET     PCQ    SECOND 

Fig>  47.— Showing  Head  at  the  Kilbourn  Dam  Under  Various  Conditions  of 

Flow. 


98  Water  Power. 

Curve")  at  Kilbourn.  On  this  diagram  has  also  been  platted  sev- 
eral discharge  curves,  two  being  for  a  weir  of  300  feet  in  length 
and  two  for  a  weir  of  350  feet  in  length.  Both  weir  curves  in  the 
upper  set  are  based  on  the  assumption  that  the  entire  flow  of  water 
is  passing  over  the  weir.  The  crest  of  the  dam  is  shown  as  raised 
to  gauge  19,  and  the  distance  between  the  rating  curve,  which  now 
represents  the  height  of  the  tail  water,  and  the  weir  discharge 
curves,  which  represent  the  height  of  the  head  water  (with  two  dif- 
ferent lengths  of  weir)  under  different  conditions  of  flow,  will  show 
the  heads  that  obtain  at  all  times  under  these  assumptions. 

The  entire  discharge  of  the  stream,  however,  will  not  pass  over 
the  dam  except  when  the  plant  is  entirely  shut  down,  which  would 
seldom  be  the  case.  The  essential  information  which  is  desired 
therefore  is  the  available  head  when  the  plant  is  in  active  operation. 
At  the  Kilbourn  plant  the  discharge  of  the  turbines  to  be  installed 
under  full  head  will  be  7,000  cubic  feet  per  second,  hence,  with  the 
plant  in  full  operation,  this  quantity  of  water  will  be  passing 
through  the  wheels.  Therefore  in  determining  the  relation  between 
head  water  and  tail  water  it  must  be  considered  that  with  a  flow  of 
7,000  cubic  feet  per  second,  the  water  surface  above  the  dam  will 
be  at  the  elevation  of  its  crest,  no  flow  occurring  over  the  spillway, 
and  that  only  the  flows  greater  than  this  amount  will  pass  over 
the  dam.  Another  curve  for  each  weir  has  therefore  been  added 
to  the  diagram  in  which  the  zero  of  the  weir  curves  is  platted 
from  the  point  where  the  line  representing  the  height  of  the  dam 
(elevation  19)  intersects  the  line  representing  a  discharge  of  7,000 
cubic  feet  per  second.  From  this  diagram  (Fig.  47)  it  will  be  seen 
that  other  heads,  shown  in  Table  VIII,  will  obtain  under  various 
conditions  of  flow. 

It  will  readily  be  seen  that  the  line  representing  the  height  of 
the  dam  is  not  essential  and  that  the  curves  may  be  platted  relative 
to  each  other,  leaving  the  height  of  the  dam  out  of  the  question 
entirely  and  indeterminate.  A  curve  constructed  on  this  basis  but 
otherwise  drawn  in  the  same  manner  as  in  Fig.  47,  is  shown  in  Fig. 
48.  In  Fig.  48,  wherever  the  weir  or  head  water  curves  pass  above 
the  tail  water  curve,  it  shows  that  an  increase  in  the  head  will  re- 
sult under  the  corresponding  condition  of  flow  and  wherever  they 
pass  below  such  curve,  it  shows  that  a  decrease  in  the  head  will 
result  under  the  corresponding  condition  of  flow,  the  amount  of 
which  is  clearly  shown  by  the  scale  of  the  diagram.  Consequently, 
having  given  the  height  of  the  dam  above  tail  water  at  the  point 


The  Graphic  Representation  of  Head.  99 

of  no  discharge,  the  head  available  under  any  other  condition  can 
be  immediately  determined  from  the  diagram. 

From  this  diagram  the  changes  in  head  (as  shown  in  table  IX) 
can  be  determined  and  these,  with  a  17  foot  dam,  will  give  the  total 

TABLE  VIII. 

Gauge  heights  and  heads  available  at  Kilboum  Dam  under  various  conditions 
of  flow,  with  a  length  of  spillway  of  300  and  350  feet. 


HEAD^ 

WATER 

HEAE 

WITH 

Flow  in  cubic  feet 
per  second. 

300 
ft.  dam. 

350 
ft.  dam. 

Tail 
Water. 

300 
ft.  dam. 

350. 
ft.  dam. 

7000.... 

19 

19 

0 

1  7 

14000  

22  9 

29  °> 

*>   1 

170 

Ll 
1  7    9 

21000  

25  2 

24  6 

Q 

179 

I/  ./ 
1  K    A 

28000  

27 

26  9 

mQ 

1R   7 

ID.O 

-ICQ 

0*5000  

28  5 

27  7 

I9  2 

ifi  *i 

I  C      ft 

42000  

30.2 

29  3 

13  6 

ifi  fi 

i  c    7 

49000  

31.5 

30  4 

14  7 

Ifi  8 

ic    7 

56000  

32  7 

31  6 

1  ^  fi 

17   1 

-ICQ 

10.  o 

heads  available  under  various  conditions  of  flow  as  shown  in  the 
last  two  columns.  These  heads  will  be  seen  to  correspond  with  the 
heads  given  in  table  VIII. 


DISCHARGE    OF      WISCONSIN     RIVER     AT     KILBOURN  —IN    CUBIC    FT.      PER    SEC. 

Fig.  48.— Showing  Change  in  Head  at  Kilbourn  Dam  Under  Various  Condi- 
tions of  Flow. 


100 


Water  Power. 


TABLE  IX. 

Changes  in  head  at  Kilbourn  Dam  with  lengths  of  crest  of  SOO  and  350  feet  and 
under  various  conditions  of  floiv  with  resulting  total  available  head  ivith  17  ft. 
dam. 


Flow  in  cubic  feet 
.  per  second. 

CHANGES  IN  HEAD  WITH 

TOTAL  HEAD  WITH 

300 
ft.  dam. 

350 
ft.  dam. 

300 
ft.  dam. 

350 
ft.  dam. 

7000  ...... 

0 
+    .8 
+    .2 
—  .3 
—  .5 
—  .4 
—  .2 
+    .1 

0 
+   .2 
—  .4 
—1.1 
—1.5 
—1.3 
—1.3 
—1.2 

17 
17.8 
17.2 
16.7 
16.5 
16.6 
16.8 
17.1 

17 
17.2 
16.6 
15.9 
15.5 
15.7 
15.7 
15.8 

14000  

21000  

28000  

35000 

42000  .  .     . 

49000  

56000  

60.  Effects  of  Design  of  Dam  on  Head. — It  should  be  noted  in 
both  of  the  last  diagrams  that  the  height  of  the  water  above  the 
dam  is  readily  controlled  by  a  change  in  the  form  and  length  of 
the  weir;  that  a  contraction  in  the  weir  length  produces  a  corre- 
sponding rise  in  the  head  waters  as  the  flow  increases,  while  the 
lengthening  of  the  weir  will  reduce  the  height  of  the  head  water 
under  all  conditions  of  flow.     The  physical  conditions  relative  to 
overflow  above  the  dam  will  control  the  point  to  which  the  head 
waters  may  be  permitted  to  rise  and  will  modify  the  length  and  the 
construction  of  the  dam.    Where  the  overflow  must  be  limited,  the 
waters,  during  flood  times,  must  be  controlled  either  by  a  suffi- 
cient length  of  spillway  or  by  a  temporary  or  permanent  reduction 
in  the  height  of  the  dam  such  as  the  removal  of  flash  boards,  the 
opening  of  gates,  or  by  some  form  of  movable  dam. 

Having  determined  the  head  available  at  all  conditions  of  river 
flow,  the  hydrograph,  as  previously  shown,  may  be  modified  to  show 
the  actual  power  of  the  river  under  the  varying  conditions  of  flow. 
The  vertical  scale,  in  this  case,  instead  of  being  uniform  must  be 
variable  as  the  head  varies.  Fig.  49  shows  graphically  the  variation 
in  the  continuous  theoretical  power  of  the  river  taking  into  con- 
sideration the  variation  in  head  which  will  actually  occur.  Com- 
pare this  hydrograph  with  Fig.  40  in  which  no  variation  in  head 
is  considered. 

6 1.  Effect  of  Head  on  the  Power  of  the  Plant. — It  is  important 
at  this  point  to  take  into  consideration  the  effect  of  head  and  flow 
on  the  actual  power  of  the  plant.    In  most  rivers,  under  flood  condi- 


Effects  of  Design  of  Dam 'on  Ke'ad. 


101 


m  ^  n  cu 

31IW    3UVntlS    U3d    QND33S    H3d    133J    318(13    Nl 


39UVH3SIO 


IO2  Water  Power. 

tions,  'the  power  theoretically  *  available  is  largely  increased,  for, 
while  the  head  may  diminish,  the  flow  becomes  so  much  greater 
that  the  effect  of  head  on  the  theoretical  power  is  more  than  off- 
set thereby.  Practically,  however,  the  conditions  of  head  under 
which  a  given  water  wheel  will  operate  satisfactorily  (i.  e.  at  a 
fixed  speed)  are  limited,  and,  while  the  theoretical  power  of  the 
river  may  radically  increase,  the  power  of  the  plant  installed  under 
such  conditions  will  often  seriously  decrease,  and  under  extreme 
conditions  may  cease  entirely.  The  discharging  capacity  of  any 
opening  is  directly  proportional  to  the  square  root  of  the  head,  and 
the  water  wheel,  or  water  wheels,  simply  offers  a  particular  form 
of  opening,  or  openings,  and  operates  essentially  under  this  general 
law.  With  a  fixed  efficiency,  therefore,  the  power  which  may  be 
developed  by  a  water  wheel  is  in  direct  proportion  to  its  discharging 
capacity  and  to  the  available  head.  Hence,  the  power  of  the  wheel 
decreases  as  the  product  of  these  two  factors,  and  therefore  the 
power  available  under  conditions  of  high  flow  and  small  head  are 
much  less  than  where  the  head  is  large  and  the  total  flow  of  the 
river  is  less.  The  only  way,  therefore,  to  take  advantage  of  the 
large  increase  in  theoretical  power  during  the  high  water  condi- 
tions is  to  install  a  surplus  of  power  for  the  condition  of  average 
water.  This  may  sometimes  be  done  to  advantage,  but  its  extent 
soon  reaches  a  practical  limitation  on  account  of  the  expense.  It 
often  becomes  desirable  to  take  care  of  such  extraordinary  condition 
by  the  use  of  supplemental  or  auxiliary  power.  Such  power  can 
usually  also  be  applied  during  conditions  of  low  water  flow  when 
the  power  is  limited  by  the  other  extreme  of  insufficient  water  under 
maximum  head. 

In  considering  the  effect  of  head  on  the  power  of  a  plant,  it  is 
necessary  to  understand  that  water  wheels  are  almost  invariably 
selected  to  run  at  a  certain  definite  speed  for  a  given  power  plant 
and  cannot  be  used  satisfactorily  unless  this  speed  can  be  main- 
tained. Also  that  any  wheel  will  give  its  best  efficiency  at  a  fixed 
speed  only  under  limited  changes  in  head.  If  the  head  changes 
radically,  the  efficiency  changes  as  well  and  this  fact  becomes 
more  serious  under  a  reduction  in  head.  As  the  head  is  reduced, 
the  discharging  capacity  of  the  wheel  and  its  efficiency  is  also 
rapidly  reduced  so  that  the  power  of  the  wheel  decreases  more 
rapidly  than  the  reduction  in  the  discharging  capacity  would 
mdicate.  When  the  reduction  of  head  reaches  a  certain  point  the 
wheel  is  able  to  simply  maintain  its  speed  without  developing 


Relations  of  Power,  Head  and  Flow.  103 

power,  and  when  the  head  falls  below  that  point,  the  speed  can  no 
longer  be  maintained.  It  is  therefore  plain  that  when  the  head  of 
a  stream  varies  greatly,  it  becomes  an  important  and  difficult  matter 
to  select  wheels  which  will  operate  satisfactorily  under  such  varia- 
tions, and,  when  the  variations  become  too  great,  it  may  be  prac- 
tically or -financially  impossible  to  do  so.  This  subject  is  discussed 
at  length  in  a  later  chapter,  but  is  called  to  the  attention  of  the 
engineer  as  an  important  matter  in  connection  with  the  study  of 
head. 

62.  Graphical  Investigation  of  the  Relations  of  Power,  Head  and 
Flow. — The  relation  of  head  and  flow  to  the  horse  power  of  any 
stream  on  which  a  dam  has  been  constructed,  may  be  graphically 
investigated  and  determined  by  a  diagram  similar  to  Fig.  50.  On 
this  diagram  are  platted  hyperbolic  lines  marked  "horse  power 
curves"  which  show  the  relation  of  horse  power  to  head  and  flow 
within  the  probable  limits  of  the  conditions  at  Three  Rivers,  Mich. 
These  lines  are  drawn  to  represent  the  actual  horse  power  of  a 
stream  under  limited  variations  in  head  and  flow  and  on  the  basis 
of  a  plant  efficiency  of  75  per  cent.  These  heads,  which  actually 
obtain  at  the  Three  Rivers  dam,  were  observed  under  three  condi- 
tions of  flow,  and  these  observations  were  platted  on  the  diagram 
at  e  e  e  and  a  .curve  was  drawn  through  them.  From  the  intersec- 
tion of  this  curve  with  the  horse  power  curves,  the  actual  power 
of  the  river  available  under  the  actual  variations  of  head  and  flow, 
is  determined.  These  measurements  were  taken  with  all  of  the 
water  passing  over  the  dam. 

Let-  us  assume  that  it  is  desired  to  investigate  the  effect  of  an 
installation  of  wheels,  using  600  cubic  feet  per  second,  under  a 
nine  foot  head.  Under  these  conditions  part  of  the  water  will  pass 
through  the  turbines  instead  of  over  the  crest  of  the  dam,  the 
available  head  will  therefore  be  somewhat  reduced,  and  the  power 
curve  of  the  river,  under  these  new  conditions,  is  shown  on  the 
diagram  by  the  curve  f  f  f .  This  curve  was  platted  from  the  curve 
e  e  e  by  computing  the  amount  the  head  on  the  crest  of  the 
dam  would  be  lowered  at  different  stages  of  the  river  by  diverting 
through  the  wheels  the  quantity  of  water  which  they  will  pass  under 
the  reduced  head.  The  actual  power  of  the  river  at  different  heads 
and  under  these  conditions  is  shown  by  the  intersection  of  the  line 
f  f  f  with  the  horse  power  curve,  and  the  actual  power  of  the  pro- 
posed plant  under  various  conditions  of  flow  is  obtained  by  pro- 


104 


Water  Power. 


2200  -  * 


I  I  I 

CURVE:     SHOWING      RELATIONS     or 
POWER  .   DISCHARGE.     MMD 


u 


B.5  9.0  9.5  ID.Q  IQ.5 

TOTAL  FALL  FROM  ABOVE  DAM  TO  MOUTH  OF  TAIL   RACE 

Fig.  50. — Graphical  Study  of  Head. 

jecting  the  point  of  intersection  of  the  discharge  line  with  the 
line  f  f  f  on  the  turbine  discharge  line  d  d. 

Thus,  with  a  flow  of  600  cubic  feet  per  second,  the  power  of  the 
plant  would  be  about  470  horse  power,  while,  with  a  flow  of 
2,100  feet  per  second,  the  power  of  the  plant  would  decrease  to  about 
420  horse  power.  At  discharges  below  600  cubic  feet  per  second, 
the  head  would  drop  rapidly  unless  a  portion  of  the  installation  was 
shut  down. 

63.  Graphical  Study  of  Power  at   Kilbourn. — A   more   detailed 


Relations  of  Power,  Head  and  Flow. 


105 


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T-H- 
IO 

60. 

5- 


ro6  Water  Power. 

study  of  head  in  connection  with  the  conditions  at  Kilbourn,  Wis- 
consin, is  illustrated  by  Figures  51  and  52.  In  Figure  51  the  theo- 
retical horse  power  of  any  stream  resulting  from  any  variation  be- 
tween the  head  and  flow  is  shown  by  the  hyperbolic  curves  drawn 
from  the  upper  to  the  right  hand  side  of  the  diagram.  Figure  47, 
already  considered,  shows  the  relation  of  the  head  and  tail  water  at 
Kilbourn,  where  a  dam  with  a  crest  350  feet  in  length  is  projected. 

The  curve  on  Figure  51  marked  "Height  of  crest  of  dam  above 
tail  water"  was  obtained  by  subtracting  the  height  of  tail  water 
at  the  various  river  stages,  as  given  by  the  rating  curve  of  the 
river,  from  the  height  to  wrhich  the  dam  is  to  be  constructed  and 
platting  the  same  in  their  correct  position  on  the  diagram.  The 
dam  here  considered  is  17  feet  in  height  above  average  water  or 
with  its  crest  at  elevation  19  on  the  gauge.  The  curve  on  the  right 
marked  "Fall  over  dam, — all  gates  closed",  is  constructed  in  the 
same  manner  by  laying  off  as  abscissas  the  actual  head  as  deter- 
mined from  Fig.  47  under  various  conditions  of  flow  when  the 
whole  discharge  of  the  river  is  passing  over  the  dam.  The  ab- 
scissas, therefore,  between  these  two  curves  show  the  head  on 
the  crest  of  the  dam  when  the  whole  discharge  of  the  river  is 
passing  over  the  dam.  For  any  given  river  discharge  (as  for  in- 
stance 16,000  cubic  feet  per  second)  the  total  fall  can  be  obtained 
(in  this  case  18.8)  and  the  theoretical  horse  power  of  the  river  (in 
this  case  34,000  horse  power)  can  be  determined  by  finding  the 
intersection  of  the  line  for  16,000  cubic  feet  per  second  with  the 
curve  marked  "Fall  over  dam, — all  gates  closed",  and  determining 
the  relation  of  this  point  to  the  power  curves.  This  relation  is 
more  clearly  indicated  by  the  first  scale  to  the  right. 

64.  Power  of  the  Kilbourn  Wheels  Under  Variations  in  Flow. — 
When  the  gates  to  the  turbines  are  open  a  less  quantity  of  water 
will  flow  over  the  dam  and  the  head  on  the  crest  will  therefore  be 
•diminished.  The  amount  of  water  which  will  pass  through  the  pro- 
posed installation  under  various  heads,  is  shown  by  the  curve 
marked  "Discharge  24-57"  turbines."  The  intersection  of  this  curve, 
with  the  discharge  lines,  at  all  points  to  the  left  of  the  curve  marked 
"Height  of  crest  of  dam  above  tail  water"  indicates  that  such  flows 
will  pass  through  the  wheels  at  the  head  indicated  by  the  point  of 
intersection.  The  practical  limit  of  the  turbine  capacity  is  the 
discharge  indicated  by  the  point  of  intersection  of  the  turbine 
discharge  curve  with  the  "Height  of  crest  of  dam  above  tail  water". 
It  will  be  noted  that  this  intersection  shows  a  maximum  discharge 


Effects  of  Low  Water  Flow,  icy 

of  7,000  cubic  feet  per  second  under  a  head  of  17  feet.  A  further 
increase  in  the  discharge  of  the  river  up  to  8,700  cubic  feet  per  sec- 
ond, causes  an  increase  in  the  head,  which  is  found  by  following 
upward  the  curve  marked  "Head  24  turbines"  to  the  point  m  where 
a  maximum  head  is  indicated.  The  discharge  from  the  turbines 
under  this  condition  increases  but  slightly  and  is  indicated  by  the 
vertical  projection  of  the  point  of  greatest  head  (m)  on  the  turbine 
discharge  line  (at  n)  which  is  so  slightly  above  the  7,000  cubic  feet 
line  as  to  be  hardly  distinguishable  on  the  diagram. 

The  power  of  the  plant  depends  upon  the  head  and  the  discharge 
through  the  wheels,  hence  the  theoretical  power  which  might  be 
developed  by  the  24  turbines  with  a  flow  of  8,700  cubic  feet  per 
second  would  be  about  13,800  horse  power,  which  can  be  deter- 
mined by  calculation  or  is  shown  by  the  relation  of  the  point  n  to 
the  power  curves.  The  actual  value  of  these  various  points  is  more 
clearly  shown  on  the  second  scale  to  the  right,  marked  "Theoretical 
power  of  plant  24-57"  turbines".  A  further  increase  in  the  dis- 
charge decreases  the  head  until  for  the  24  turbines  a  minimum  is 
reached  at  a  discharge  of  42,500  cubic  feet  per  second.  Under  this 
condition  of  head  the  discharge  through  the  wheels  has  also  been 
somewhat  reduced,  and  the  corresponding  rmrse  power  is  reduced 
to  11,300  as  shown  by  the  intersection  of  the  discharge  curve  and 
the  line  indicating  the  head  existing  under  these  conditions. 

65.  Effects  of  Low  Water  Flow. — In  the  case  of  low  water  when 
the  flow  is  not  sufficient  to  maintain  the  flow  over  the  dam,  if  the 
turbines  are  run  at  full  capacity,  the  water  level  behind  the  dam 
will  drop  until  a  point  of  equilibrium  is  attained  where  the  head  is 
just  sufficient  to  force  the  entire  discharge  through  the  turbines. 
As  the  water  level  is  lowered  below  the  crest,  the  power  of  the  plant 
rapidly'  diminishes  owing  to  the  great  decrease  in  the  head  for  a 
small  decrease  in  the  flow.  When  the  head  decreases  beyond  a 
certain  point  the  power  of  the  plant  may  be  increased  by  closing 
some  of  the  gates  of  the  turbines  until  the  discharge  through  the 
turbines  is  less  than  the  discharge  of  the  river,  when  the  head  will 
increase  by  the  backing  up  of  the  water  behind  the  dam. 

Thus  it  will  be  seen  by  the  diagram  that,  with  only  6,000  cubic  feet 
per  second  flowing  in  the  river,  if  all  of  the  turbines  are  operated 
the  head  will  drop  to  about  12.7  feet,  and  the  power  of  the  plant 
under  this  head  and  flow  would  be  about  8,660  horse  power.  If, 
under  these  conditions,  one  unit  of  six  turbines,  amounting  to  one- 
fourth  of  the  plant,  is  shut  down,  the  water  will  rise  until  the  head 


io8  Water  Power. 

is  increased  to  about  18  feet.  Under  these  conditions  about  800 
cubic  feet  per  second  of  this  water  will  waste  over  the  dam,  and  the 
power  developed  by  the  remaining  portion  of  the  plant  will  be  10,630 
horse  power,  or,  about  2,000  horse  power  more  with  one  unit  shut 
down  and  with  the  resulting  head  than  with  all  units  in  operation 
and  the  consequent  lower  head.  The  above  discussion  simply  illus- 
trates the  point  that  it  is  rarely  desirable  to  draw  down  the  head 
of  an  operating  plant,  at  least  to  any  great  extent,  for  the  sake  of 
operating  a  greater  number  of  wheels,  unless  this  is  done  for  the 
purpose  of  impounding  the  night  flow  for  use  during  the  day  or  at 
times  of  maximum  load.  Even  in  this  case  too  great  a  reduction 
in  the  head  is  undesirable  and  uneconomical. 

66.  Effects  of  Number  of  Wheels  on  Head  and  Power. — Fig.  52 
is  an  enlarged  section  of  that  part  of  Fig.  51  shown  by  the  dotted 
lines.  This  diagram  shows  how  the  head  on  the  wheels  may  be 
maintained  by  shutting  off  some  of  the  wheels  in  case  the  flow  be- 
comes so  small  as  to  entirely  pass  the  wheels  and  thus  reduce  the 
head,  as  described  above.  It  will  be  noted  that  with  a  total  instal- 
lation of  48  wheels,  by  closing  the  gates  of  two  wheels  at  a  time, 
the  variation  in  the  head  would  be  only  a  fraction  of  a  foot  until  as 
ma^y  as  24  wheels  ahe  closed.  Hence  it  will  be  seen  that  when  the 
power  has  been  decreased  by  a  rduction  of  head,  the  wheels  should 
be  closed  off  until  the  same  power  can  be  secured  by  the  less  num- 
ber of  wheels  operating  with  the  highest  head  that  is  available  with 
the  given  discharge  of  the  river.  As  the  lower  flows  of  the  river 
are  reached  great  fluctuation  in  the  head  will  occur  with  the  opera- 
tion of  the  turbine  gates.  This  diagram  shows  the  actual  delivered 
power  of  the  plant  and  is  based  on  a  plant  efficiency  of  75  per  cent. 
The  power  obtained  for  a  given  discharge  is  therefore  less  than 
shown  by  Fig.  51. 

In  order  to  secure  more  accurate  results  a  small  correction  for 
the  variations  in  efficiency  under  the  variations  in  head  may  some- 
times be  desirable.  '  In  the  problem  under  consideration  this  is 
unnecessary  on  account  of  the  small  variation  which  takes  place. 
However,  when  the  variations  in  head  are  considerable,  this  correc- 
tion is  essential  if  a  close  estimate  of  power  at  different  heads  is 
desired.  Figure  53  is  a  power  hydrograph  similar  to  those  already 
discussed  but  with  such  changes  in  the  scale  as  to  show  the  con- 
tinuous power  that  could  have  been  developed  by  these  four  groups 
of  turbines  at  Kilbourn,  Wisconsin,  during  the  year  1904,  under 


Effects  of  Number  of  Wheels  on  Head  and  Power         109 


10000 


14000 


12000    ^^ 


10000 


8000 


6COO 


4000 


2000    — 


14 


15 


.16 


19 


17  18 

Head  in  Feet 

Note— H.  P.  Curves  are  based  on   75$  efficiency 

Fig.  52. — Relation  of  Number  of  Wheels  to  Power  and  Head. 

the  variations  in  head  which  would  actually  have  occurred  with  the 
dam  it  is  proposed  to  construct. 

From  the  previous  discussion  of  the  conditions  at  Kilbourn  it 
is  seen  that  with  a  dam  with  fixed  crest  the  variations  in  head, 
due  to  variations  in  flow,  are  comparatively  small.  Consequently 
the  power  of  the  wheel  to  be  installed  will  not  decrease  with  an  in- 
crease in  flow  to  as  great  an  extent  as  usually  occurs  in  water 
power  plants.  If  a  system  of  flash  boards  or  an  adjustable  crest  is 
found  desirable  in  order  to  prevent  overflow  at  times  of  flood,  the 
power  of  the  plant  when  these  are  lowered  will  be  still  further 
reduced. 

The  hydrograph  may  be  utilized  for  more  detailed  analysis  of 
water  power  questions  and  will  be  further  discussed  in  a  future 
chapter. 


no 


Water  Power. 


93Miaani 

o 


ivDii3U03H± 

n 


CHAPTER  VI. 

RAINFALL. 

67.  Importance  of  Rainfall  Study. — The  influence  of  rainfall  on 
the  flow  of  streams  is  so  direct  that  those  unfamiliar  with  the  sub- 
ject are  apt  to  assume  that  the  relation  may  be  represented  by 
some   simple  expression  and  that,  therefore,   if  the  rainfall  for  a 
period  of  years  be  known,  the  corresponding  stream  flow  may  be 
directly  and  readily  calculated  therefrom.     With  only  a  brief  famil- 
iarity with  the  subject  it  is  evident  that  no  such  simple  relation  ex- 
ists.    The  relationship  is,  in  fact,  complicated  by  a  multiplicity  of 
other  physical  conditions  which  have  an  important  if  not  an  equal 
influence. 

Observations  of  stream  flow  are  quite  limited  both  in  time  and 
geographical  extent  while  the  observations  of  rainfall  have  extended 
over  a  long  period  of  time  and  the  points  of  observation  are  geo- 
graphically widely  distributed.  If,  therefore,  it  is  possible  to  trace 
such  relationship  between  the  flow  of  streams  and  the  rainfall 
and  other  physical  conditions  on  the  drainage  areas  as  will  enable 
the  engineer  to  calculate  the  flow  even  approximately,  such  relation- 
ships become  of  great  value  to  the  water-power  engineer,  on  ac- 
count of  the  lack  of  other  more  definite  information.  It^is  there- 
fore important  that  the  engineer  inform  himself  as  fully  as  pos- 
sible on  the  relations  that  exist  between  rainfall  and  stream  flow 
and  the  modifications  of  those  relations  by  other  physical  factors. 
By  such  means  the  information  regarding  rainfall,  already  recorded 
for  long  terms  of  years,  may  be  applied  to  the  problem  of  stream 
flow  in  which  the  engineer  is  more  directly  concerned.  For  this 
reason  the  subject  of  rainfall  is  here  discussed  in  as  much  detail 
as  the  space  will  permit. 

68.  Distribution  of  Rainfall. — A  continuous  circulation  of  water 
is  in  progress  on  the  earth's  surface.     The  evaporation  from  the 
water  and  moist  earth   surfaces  rises  into  the  atmosphere  in  the 


129-        127'        125"       123'        121°        119°       117°        115°       113°       111         109°        ™7°       105°      103°       101'       90'       95 


119°  117°  US'  H3-  lir  109°  107 


Jtf0       03°        91°        89°       87°        85°        83" 


OP  THE 

UNITED^STATES 


ix4 


Rainfall. 


1895 


1896 


1897 


1898 


IQ99 


•1900 


E325  TO  30M30  TO  35^33  TO  40^0VrB  40 
llNCHES     I!      HI  INCHES     Y//A  INCHES  .  E    3  INCHES  .  gra.NCHES  .  CINCHES  .  ^  INCHES  . 


Fig.  55.— Distribution  of  Total  Annual  Rainfall  in  Wisconsin. 


Distribution  of  Annual  Rainfall  in  Wisconsin.  115 


1901 


1902 


1903 


1904 


1905 


UNDERI5     Ijij    ISTOaok%//320T025 
INCHES.      I      |j    INCHES.  Y///A  INCHES 


23  TO  30 
INCHES 


30  TO  35 
INCHES 


AVERAGE 

J35  TO  40  | 
ilNCHES 


| OVER  40 
llNCHES 


Fig.  56. — Distribution  of  Total  Annual  Rainfall  in  Wisconsin. 


1. 1 6  Rainfall. 

form  of  vapor,  partially  visible  as  clouds,  mist  and  fog,  and  is 
afterwards  precipitated  as  rain  and  dew.  The  distribution  of  rain- 
fall on  the  earth's  surface  is  by  no  means  uniform.  An  examina- 
tion of  Fig.  54,  which  is  a  map  showing  the  average  distribution  of 
the  annual  rainfall  in  the  United  States,  will  show  how  greatly  the 
average  annual  rainfall  differs  in  various  parts  of  the  United  States. 
The  local  variation  in  the  average  annual  rainfall  in  the  United 
States  is  from  a  minimum  of  no  rainfall,  during  some  years  in  the 
desert  regions,  to  an  occasional  maximum  of  more  than  one  hun- 
dred inches  in  the  extreme  northwest.  From  this  map  it  will  be 
noted  that  from  the  Mississippi  westward  the  lines  of  equal  rain- 
fall are  approximately  north  and  south  and  parallel  with  the  moun- 
tain ranges.  In  the  Southern  states,  east  of  Texas,  they  are  ap- 
proximately parallel  with  the  Gulf  of  Mexico,  and  on  both  the  At- 
lantic and  Pacific  coasts  they  are  approximately  parallel  with  the 
coast  lines.  At  various  points  in  the  United  States  other  influences 
come  into  play  and  greatly  modify  the  general  distribution  as  above 
outlined.  In  a  general  way  the  rainfall  may  be  said  to  be  in- 
fluenced by  the  topography  of  the  continent  and,  to  a  considerable 
extent,  by  its  altitude.  In  general,  the  rainfall  decreases  as  the 
elevation  above  sea  level  increases,  although  in  some  cases  the  op- 
posite effect  holds.  This  general  law  seems  to  be  substantiated  by 
reference  to  the  annual  rainfall  map.  In  passing  along  the  parallel 
of  40°  as  we  ascend  from  the  Mississippi  River  to  the  western 
mountains  the  annual  rainfall  decreases  from  about  35  inches  an- 
nually to  10  inches  or  less.  On  the  other  hand,  a  reference  to  our 
Western  coast  will  show  that  some  of  the  heaviest  rainfalls  that 
occur  are  due  to  precipitation  caused  by  the  moist  winds  from  the 
Pacific  striking  the  higher  mountain  ranges.  This  is  a  local  condi- 
tion, however,  and  is  quite  different  in  its  character  from  the  gen- 
eral law  above  stated.  The  mountain  ranges  along  the  Pacific 
coast  which  intercept  the  moisture  from  the  Pacific  and  cause  the 
heavy  rainfalls  in  the  higher  mountain  areas  are  also  the  direct 
cause  of  the  small  rainfall  in  the  arid  regions  lying  east  of  these 
mountains. 

69.  The  Rainfall  Must  be  Studied  in  Detail. — The  map  of  average 
annual  rainfall  is  of  value  only  for  a  general  view  of  the  subject. 
For  special  purposes  a  detail  study  of  the  local  variations  from  the 
average  conditions  is  necessary.  Great  variations  take  place  in  the 
annual  rainfall  of  every  locality.  Sometimes  the  annual  rainfall 
will  be  for  a  series  of  years  considerably  below  the  average,  and 


Distribution  of  Weekly  Rainfall  in  Wisconsin.  117 


MAY    13   TO    MAY  20 


MAY    20  TO  MAY    27 


MAY    27   TO   JUNE    3 


JUNE     3     TO    JUNE    10 


JUNE    10   TO    JUNE    17 


JUNE    17    TO    JUNE    24 


INCHES         IN         DEPTH 


OT0.25"  .25T0.50  .SO"TO.7S"  .75"TO  \". 

Fig.  57.— Distribution  of  Weekly  Rainfall  in  Wisconsin 


u8 


Rainfall. 


Fig.  58.— Rainfall  Conditions  in  the  United  States  at  8  A.  M.,  July  10th,  1907. 


Fig.  59.— Rainfall  Conditions  in  the  United  States  at  8  A.  M.,  July  17th,  1907. 


Local  Variations  in  Annual  Rainfall.  119 

then  for  a  number  of  years  the  average  may  be  considerably  ex- 
ceeded. No  general  law  seems  to  hold,  however,  in  regard  to  this 
distribution  and  the  variation  seems  to  occur  either  without  law  or 
by  reason  of  laws  so  complicated  as  to  defy  determination.  The 
variations  in  the  distribution  of  the  annual  rainfall  in  the  State  of 
Wisconsin  for  eleven  years  are  shown  by  Figs.  55  and  56.  From 
these  maps  can  be  clearly  seen  how  greatly  the  distribution  of  rain- 
fall throughout  the  state  differs  in  different  years  from  the  average 
annual  rainfall  as  shown  on  the  last  map  of  the  series.  It  should 
also  be  noted  that  in  the  same  manner  these  annual  rainfall  maps 
are  the  results  of  the  summation  of  an  irregular  distribution  of 
numerous  rainstorms,  the  irregularities  of  which  can  perhaps  be 
more  clearly  shown  by  the  maps  on  Fig.  57  which  show  the  weekly 
distribution  of  rainfall  in  Wisconsin  for  six  consecutive  weeks  in 
May  and  June,  1907.  All  such  maps  are  but  the  result  or  sum- 
mation of  individual  rainstorms  which  occur  during  the  period 
considered.  Individual  rainstorms  never  occur  twice  over  exactly 
the  same  geographical  extent  of  territory  nor  with  equal  intensity 
at  any  points  within  the  territory  covered.  They  are  not  only 
irregular  in  their  distribution  but  progressive  in  both  their  dis- 
tribution and  intensity,  changing  from  hour  to  hour  during  their 
occurrence.  The  extent  of  a  somewhat  general  rainstorm  in  pro- 
gress at  8 :  oo  A.  M.  (Washington  time)  over  the  Northwest  on  July 
i6th,  1907,  is  shown  by  Fig.  58.  On  the  area  over  which  this  storm 
extended,  the  actual  precipitation  varied  widely  and  the  extent  of 
the  storm  rapidly  changed  from  hour  to  hour.  At  8 :  oo  A.  M.  on 
July  I7th  the  general  rainfall  had  ceased  and  the  storm -had  be- 
come localized  as  shown  by  Fig.  59.  The  varying  character  and 
extent  of  the  rainfall  as  illustrated  by  those  two  maps  show  the 
extremes  of  one  storm  which  affected  the  Northwest,  and  illustrates, 
in  a  general  way,  the  irregularity  and  lack  of  uniformity  in  rainfall 
occurrence  and  distribution. 

70.  Local  Variation  in  Annual  Rainfall. — By  reference  to  Fig.  60, 
the  variations  which  have  occurred  in  the  annual  rainfall  at  various 
localities  in  the  United  States  will  be  seen,  and  from  this  data  the 
lack  of  uniformity  in  the  annual  rainfall  will  be  more  fully  appre- 
ciated. By  an  examination  of  the  records  of  a  sufficient  number 
of  years  the  limiting  conditions  may  be  determined  and  an  ap- 
proximate determination  of  the  relation  between  the  extremely  dry 
and  extremely  wet  periods  made. 


120 


Rainfall. 


No.  Atlantic,  So  Atlantic,  St.  Lawrence,  Ohio  River, 

New  Haven,  Conn.  Augusta,  Ga.  Detroit,  Mich.  Cincinnati,  O. 


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Columbia,                        Pacific,                        Colorado,                   Great  Basin, 
Spokane,  Wash.                Sacramento,  Cal.           Phoenix,  Ariz.          Winnemucca,  Nev. 

Fig.  60. — Variation  in  Annual  Rainfall  at  Various  Points  in  the  United  States. 


Local  Variations  in  Annual  Rainfall. 


121 


Figure  61  i«  a  diagram  showing  the  fluctuations  that  have  occurred 
in  the  annual  rainfall  at  Madison,  Wisconsin,  from  1869  to  1905. 
The  variation  at  Madison  has  been  from  a  maximum  of  about 
52  inches  in  1881  to  a  minimum  of  about  13  inches  in  1895  which 
represents  a  greater  range  (4  to  i)  than  ordinarily  obtains.  As  a 
general  rule  the  maximum  may  be  stated  to  be  about  double  the 
minimum  annual  rainfall. 


FLUCTUATION     OF      ANNUAL      RAINFALL     AT      MADISON,   WIS. 

Fig.  61 

71.  Local  Variations  in  Periodical  Distribution  of  Annual  Rain- 
fall.— The  amount  of  the  annual  rainfall  is  only  one  of  the  elements 
that  influence  the  run-off.  The  time  of  occurrence  or  the  periodical 
distribution  of  the  rainfall  is  even  of  greater  importance.  The 
general  character  of  the  periodic  distribution  of  the  annual  rain- 
fall is  similar  each  year  in  each  locality,  for  the  maximum  and 
minimum  monthly  rainfalls  occur  in  each  locality  at  fairly  definite 
periods.  As  the  cycle  of  the  seasons  changes,  conditions  favorable 
or  unfavorable  to  precipitation  obtain,  and,  while  these  differ  very 
largely  from  year  to  year  and  are  subject  to  such  wide  variations 
as  to  render  the  character  somewhat  obscure,  unless  a  number  of 
seasons  are  considered,  yet  the  same  general  character  ordinarily 
prevails. 

Figure  62  shows  the  extreme  and  the  average  variation  of  the 
monthly  rainfall  at  Madison.  The  monthly  rainfall  in  the  various 
months  differs  widely  in  amount  and  is  by  no  means  proportional 
to  the  total  annual  rainfall  for  the  year.  It  is  especially  observable 
that  during  the  year  of  maximum  rainfall,  viz:  for  1881,  the  rain- 
fall for  April  was  almost  as  low  as  for  the  April  of  the  year  1895 
when  the  total  annual  rainfall  was  at  a  minimum.  It  is  also  observ- 


INCHES  OF  RAINFALL.  E 

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FLUCTUATION     OF      MONTHLY      RAINFALL     AT      MADISON,   WIS, 

Fig.  62 

able  that  the  rainfall  for  August,  1881,  was  less  than  the  rainfall  for 
August  of  1895.  Figure  63  shows  the  typical  average  monthly  dis- 
tribution of  precipitation  at  various  points  within  the  United  States, 
and  the  general  law  to  which  even  the  variations  mentioned  par- 
tially conform.  The  character  of  the  monthly  distribution  varies 
widely  at  different  locations,  but  will  be  seen  to  have  a  similar 
character  wherever  similar  conditions  prevail.  Thus  the  New  Eng- 
land States  present  a  similarity  in  the  distribution  of  the  monthly 
rainfall.  A  similarity  in  the  monthly  distribution  is  also  found, 
throughout  the  lake  region  and  the  Ohio  Valley.  The  monthly  dis- 
tribution throughout  the  Great  Plains  is  also  similar,  and  a  marked 
similarity  exists  at  points  along  the  Pacific  coast. 

72.  Accuracy  of  Rainfall  Maps  and  Records. — It  must  be  under- 
stood that  the  rainfall  maps,  showing  lines  or  belts  of  equal  rain- 
fall, are  only  approximately  correct,  and  that  it  would  be  impossible 
to  show  by  such  lines  small  differences  in  annual  rainfall  of  less- 


Monthly  Distribution  of  Rainfall. 
"Types  of  Monthly  Distribution  of  Precipitation  in  the  United  States. 

Rainfall  Distribution  in  the  U.  S.    (Percentage  of  fall  in  each  month  represented  by  heavy  lines.) 


123 


Fig.  63 


124  Rainfall. 

than  two  or  three  inches.  As  a  matter  of  fact,  the  rainfall  actually 
differs  considerably  within  comparatively  small  limits,  but  within 
such  limits  the  average  remains  fairly  constant  for  the  year  or  sea- 
son. Frequently,  however,  the  rainfall  variations  even  within 
narrow  limits  differ  widely.  Many  questions  of  importance  in  con- 
nection with  the  consideration  of  rainfall  are  still  open  to  debate 
and  are  frequently  answered  in  a  diametrically  opposite  manner  by 
data  secured  from  different  localities. 

73.  Rainfall  and  Altitude. — The   relation   of  the  rainfall  to   al- 
titude has  been  a  subject  of  frequent  discussion  and  perhaps  the 
majority  of  data  secured  tends  to  show  that  there  is  a  material 
decrease  in  the  fall  of  rain  as  the  altitude  increases,  and  this  both 
within  a  broad  area  and  with  great  changes  of  altitude  and  within 
a  limited  area  and  where  the  differences  in  altitude  are  compara- 
tively small.     Mr.  Rafter,  in  the  Hydrology  of  New  York,  points 
out  the  fact  that  in  the  State  of  New  York  the  rainfall  records 
show  both  increase  and  diminution  of  precipitation  with  increase  of 
altitude.    The  Hudson  River  catchment  area  shows  a  higher  precipi- 
tation at  the  mouth  of  the  river  than  it  does  at  its  source  in  the 
Adirondack   mountains,   while   the   Genesee   River  shows   the  op- 
posite :  that  is,  a  higher  precipitation  at  its  source  than  at  its  mouth. 
In  this  case  the  influence  of  altitude,  if  such  influence  can  be  said 
to  obtain  on  such  limited  areas,  is  overshadowed  by  other  predomin- 
ating influences.     In  this  connection  Fig.  64  is  of  interest.     This 
diagram  shows  the  variation  in  the  annual  and  monthly  rainfall 
at  three  stations  within  the  City  of  Chicago.     Curve  No.  I  shows 
the  rainfall  at  the  Auditorium  Tower,  at  an  elevation  of  233  feet 
above  the  level  of  the  city.     Curve  No.  2  shows  the  rainfall  at  the 
Chicago  Opera  House  Building,  at  an  elevation  of  132  feet.     Curve 
No.  3  shows  the  rainfall  at  the  Major  Block,  elevation  93  feet.     The 
relative  monthly  rainfall  at  these  three  stations  varies  greatly,  and, 
while  the  annual  variations  at  these  three  points, — all  of  which  are 
within   a   square   mile   in   the   business   center   of   Chicago, — differ- 
considerably  from  each  other,  still  the  difference  is  insignificant  in 
comparison  with  the  monthly  variation.  While  the  influence  of  alti- 
tude may  possibly  be  seen  in  the  annual  results  and  possibly  in 
the  monthly  results  as  shown  at  stations  one  and  three,  the  monthly 
results  at  station  two  show  no  such  effect,  or,  at  least,  the  effect  is 
greatly  obscured  by  other  influences. 

74.  Value  of  Extended  Rainfall  Records. — One  of  the  points  that 
becomes  important  in  the  consideration  of  rainfall  records  is  the 


Value  of  Extended  Rainfall  Records. 


125 


ANNUAL 
JAM.       FEB.     MAR.      APR.     MAY     JUNE      JULY      AUG.     SEPT.     OCT.       NOV.      DEC.  I    B  3 


30 


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Fig.  4$. — Monthly. and  Annual  Precipitation  of  Three  Exposures  in  Chicago, 
111.  1.  Auditorium  Tower,  Elevation  238  feet.  2.  Chicago  Opera  House 
Building,  Elevation  132  feet.  3.  Major  Block,  Elevation  93  feet.* 

length  of  time  required  to  make  such  records  safe  as  a  basis  for 
future  estimates.  This  subject  is  well  considered  in  a  paper  by 
Alexander  A.  Binnie,  member  of  The  Institute  of  Civil  Engineers, 
published  in  the  Proceedings,  Vol.  109,  'pages  89  to  172.  Mr. 
Binnie's  conclusions  are  that: 

"Dependence  can  be  placed  on  any  good  record  of  25  years'  dura- 
tion to  give  a  mean  rainfall  correctly  within  2  per  cent  of  the  truth." 

Mr.  Rafter,  after  reviewing  this  paper,  concluded,  that: 

"For  records  from  20  to  35  years  in  length  the  error  may  be 
expected  to.  vary  from  3.25  per  cent  down  to  2  per  cent,  and  that 
for  shorter  periods  of  5  to  10  and  10  to  15  years  the  probable  ex- 
treme deviation  from  the  mean  would  be  15  per  cent  to  4.75  per 
cent  respectively." 

Mr.  Henry  from  his  examination  of  this  question  in  reference  to 
various  localities  has  drawn  the  following  conclusion: 

For  a  ten  year  period  the  following  variations  from  normal  have 
occurred : 

New  Bedford +  16  per  cent.  —  11  per  cent. 

Cincinnati +20        "  —17        " 

St.  Louis +17        "  —13        " 

Fort  Leavenworth +16        "  —18 

San  Francisco..  +    9  — 10        " 


Reproduced  from  original  slide  published  by  Geographical  Society  of  Chicago. 


126  Rainfall. 

For  a  25-year  period  Mr.  Henry  found  that  the  extreme  variation 
was  10  per  cent  both  at  St.  Louis  and  New  Bedford,  and  reached 
the  conclusion  that  at  least  35  to  40  years'  variations  are  required 
to  obtain  a  result  that  will  not  depart  more  than  -j-  or  — 5  per  cent 
from  true  normal.  The  average  variation  of  the  35-year  period  Mr. 
Henry  found  to  be  -f-  or  — 5  per  cent  and  for  a  total  4O-year  period 
+  or  — 3  per  cent. 

75.  Accuracy  in  Rainfall  Observation. — It  must  also  be  under- 
stood that  on  account  of  the  marked  variations  which  actually  occur 
in  rainfall  within  limited  areas  and  by  reason  of  limited  difference 
of  elevation,  the  observation  of  actual  rainfall  is  not  without  its 
difficulties.     In  order  to  secure  great  accuracy  great  care  must  be 
exercised  in  the  placing  of  rain  gauges  so  that  they  may  receive 
and  record  the  rain  received  in  an  accurate  manner.     Subject,  as 
they  are,  to  considerable  variations,  it  would  seem  unwise  to  use 
great  refinement  in  the  calculations  of  rainfall,  and  in  recording 
rainfall  one   decimal  place  is  probably  all  that  is  warranted  and 
two  places  is  the  ultimate  limit  of  possible  accuracy. 

76.  District  Rainfall. — In  determining  the  average  rainfall  on  a 
drainage  area  an  extended  series  of  observations  over  the  entire 
district  considered  become  essential  and  conclusions  drawn  from 
more  limited  observations  are  subject  to  considerable  inaccuracies. 
Rainfall   stations,    distributed   as   uniformly   as   possible   over   the 
drainage  area,  should  be  selected,  and  the  average  result  of  the  ob- 
servations of  these  stations  should  be  used  as  the  basis  of  calcula- 
tion.    Possibly  a  still  more  accurate  method  of  considering  this 
subject  would  be  the   selection   of  rainfall   observations   on   each 
particular  branch  of  the  stream  considered.    The  value  to  be  given 
to  each  set  of  observations  used  should  be  in  proportion  to  the  ter- 
ritory drained  by  the  tributaries. 

77.  Study  of  Rainfall  as  Affecting  Run-off. — In  considering  the 
rainfall  on  a  district  in   relation  to  the  run-off  of  streams,   it   is 
desirable   to   study  the   rainfall   records   on   the   basis   of   what   is 
termed  "water  year".    The  water  year  for  most  of  the  area  of  the 
United  States,  instead  of  coinciding  with  the  calendar  year  may 
be  best  divided  into  periods  beginning,  approximately,  with   De- 
cember and  ending,  approximately,  with  the  following  November. 
The  first  six  months  of  this  period,  December  to  May  inclusive, 
is  termed  the  "storage"  period.     June,  July  and  August  constitute 
the  "growing"  period ;  September,  October  and  November,  the  "re- 
plenishing" period.     For  the  purpose  of  discussing  rainfall  in  its 


Mean  Monthly  Rainfall 


127 


Northern  Atlantic, 
New  Haven,  Conn, 


Southern  Atlantic, 
Augusta,  Ga, 


St.  Lawrence, 
Detroit,  Mich. 


Ohio  River, 
Cincinnati,  O. 


Eastern  Gulf, 
Montgomery,  Ala. 


Western  Gnlf, 
San  Antonio,  Tex. 


Upper  Mississippi, 
Des  Moines,  Iowa. 


Lower  Mississippi, 
Little  Rack,  Ark. 


Fig.  G5. — Mean  Monthly  Rainfall  at  Various  Points  in  the  United  States. 


128 


Rainfall. 


Topeka,  Kas. 


Missouri  River 


Helena,  Mont. 


40 


30 


Hudson  Bay, 
Moorehead,  Minn. 


Xo.  Pacific, 
Tacoma,  Wash. 


Columbia  River, 
Spokane,  Wash. 


Pacific, 
Sacramento,  Cal. 


10 


10 


Colorado  River, 
Tucson,  Ariz. 


Great  Basin. 
Winnemucca,  Nev. 


Fig.  66. — Mean  Monthly  Rainfall  at  Various  Points  in  the  United  States. 


Rainfall  on  the  Drainage  Area  of  the  Wisconsin  River.      129 


T3S.3 


IAGE    OF    STORAGE^  GROWING^  AND 


TOTAL 
ANNUAL. 


STORAGE 
PERIOD 


GROWING 
PERIOD  . 


'(REPLENISHING 
JJPERIOO. 


Fig.  G7.— Rainfall  on  the  Drainage  Area  of  the  Wisconsin  River. 


130  Rainfall. 

relation  to  run-off  it  is  desirable  to  divide  the  annual  rainfall  in 
accordance  with  these  periods.  Figures  65  and  66  show  the  average 
monthly  rainfall  at  various  points  in  the  United  States,  the  average 
rainfall  for  each  of  the  periods  above  mentioned  and  an  additional 
diagram  for  each  location  showing  the  summation  of  the  total  rain- 
fall for  each  period  of  the  water  year. 

Here  again  attention  is  called  to  the  fact  that  for  most  purposes 
of  the  engineer  the  extreme  conditions  and  the  varying  conditions 
from  year  to  year  are  of  much  greater  importance  than  the  average 
conditions  as  shown  on  these  diagrams.  Figure  67  shows  the  annual 
and  periodic  rainfall  on  the  valley  of  the  AVisconsin  River  at  three 
different  points,  the  relative  location  of  which  will  be  seen  by  ref- 
erence to  the  map  on  page  84.  The  upper  diagram  shows  the  rain- 
fall on  the  drainage  area  above  Merrill,  the  center  diagram  the  rain- 
fall above  Necedah,  and  the  lower  diagram,  the  rainfall  above  Kil- 
bourn.  In  these  three  diagrams  it  is  important  to  note  the  variation 
in  the  rainfall  condition  above  the  different  points  on  the  water- 
shed. For  example,  considering  the  entire  area  above  Kilbourn  and 
above  Necedah,  it  will  be  noted  that  the  annual  rainfall  for  1895 
was  the  lowest  within  the  period  shown,  while  for  the  area  above 
Merrill  the  rainfall  for  1892  was  the  lowest  for  the  period  dis- 
cussed. This  diagram  will  illustrate  the  fact,  which  is  manifest  on 
the  investigation  of  most  large  streams,  namely,  that  frequently 
the  intensity  of  the  rainfall  upon  part  of  the  drainage  area  is  radi- 
cally different  from  that  on  other  parts,  and  that,  consequently,  the 
various  quantities  of  rain  falling  on  a  large  watershed  tend  to 
balance  each  other  and  keep  the  total  more  constant  than  observa- 
tion at  any  one  point  would  seem  to  indicate,  so  that  the  minimum 
rainfall  at  any  one  point  on  the  area  is  not  necessarily  coincident 
with  the  minimum  rainfall  that  may  occur  at  any  other  point  or 
on  the  stream  as  a  whole.  From  this  it  is  evident  that  in  an  area 
of  any  magnitude  it  is  necessary  to  consider  the  rainfall  at  a  large 
number  of  stations  well  distributed  over  the  area. 

LITERATURE. 

GENERAL    SUBJECT    OF    RAINFALL. 

1.  U.  S.  Weather  Bureau.     Annual  Reports  and  Monthly  Weather  Reviews. 

2.  Meteorologische  Zeitschrift. 

3.  Zeitschrift  des  Osterreichen  Gesellschaft  fur  Meteorologle. 

4.  Symon's  Meteorological  Magazine. 

5.  Annucine  d3  la  Societe  Meteorogique  de  France,  Paris. 


Literature.  131 

6.  The  Royal  Meteorological  Society  of  Great  Britain.     Quarterly  Journal. 

7.  Hawksley,  Thomas.     Laws  of  Rainfall  and  Its  Utilization.     Proc.  Inst. 

C.  E.     Vol.  31,  pp.  53-59.     1871. 

8.  Binnie,  Alex.  R.    Tables  of  Mean  Annual  Rainfall  in  Various  Parts  of  the 

World,    Proc.  Inst.  C.  E.     Vol.  39,  pp.  27-31.     1874. 

9.  Schott,  C.  A.     Tables  and  Results  of  the  Precipitation  of  Rain  and  Snow 

in  the  U.  S.     Smithsonian  Contribution  to  Knowledge,  No.  222, 
1874. 

10.  Charts  and  Tables   Showing  Geological  Distribution  of  Rainfall  in  the 

U.  S.    U.  S.  Signal  Service  Professional  Paper  No.  9.    1883. 

11.  Rainfall   Observations  at   Philadelphia.     Reports   Phila.  Water  Bureau, 

1890-92.     Eng.  Record,  1891,  p.  246.     1892,  p.  360. 

12.  Binnie,   Alex.   R.      Mean   or  Average   Rainfall   and   the  Fluctuations   to 

which  It  is   Subject.     Proc.   Inst.   C.  E.     Vol.   119    (1892),   pp. 
172-189. 

13.  Waldo,  Frank.    Modern  Meteorology.    New  York,  Scribner's  Sons.     1893. 

14.  Davis,  W.  M.    Elementary  Meteorology.     Boston,  Ginn  &  Co.,  1894. 

15.  Harrington,  M.  W.     Rainfall  and  Snow  of  the  United  States.     Bulletin 

C.,  U.  S.  Weather  Bureau,  1894. 

16.  Russell,  Thomas.     Meteorology.     New  York,  MacMillan  Co.     1895. 

17.  Henry,  A.  J.    Rainfall  of  the  United  States.     Bulletin  D.,  U.  S.  Weather 

Bureau.    1897. 

18.  Turneaure  &  Russell.     Public  Water  Supplies.     Chapter  4.     New  York, 

Wiley  &  Sons.     1901. 

19.  Hann,    Julius.      Handbook   of   Climatology.'    New   York,   MacMillan   Co. 

1903. 

20.  Handbook  der  Ingenieur  Wissenschaften.    Part  3,  der  Wasserbau;  sec.  1, 

Gewasserkunde.     Leipzig,  E.  Engelmann,  1904. 

21.  Hann,  Julius.     Lehrbuch  der  Meteorologie.     Leipzig.     1906. 

EXCESSIVE  RAINFALL. 

22.  Francis,  Jas.  B.    Distribution  of  Rainfall  during  a  Great  Storm  in  New 

England  in  1869.     Trans.  Am.  Soc.  C.  E.    Vol.  77,  p.  224. 

23.  The  New  England  Rain  Storm  of  Feb.  10-14,  1886.   Eng.  News,  1886,  Vol. 

15,  p.  216. 

24.  Hoxie,  R.  L.     Excessive  Rainfalls  Considered  with  Special  Reference  to 

Their  Appearance  in  Populous!  Districts.    Trans.  Am.  Soc.  C.  E., 
p.  70.    June,  1891. 

25.  Talbot,  Arthur  N.     Rates  of  Maximum  Rainfall.     Technograph,  Univ.  of 

Illinois.     1891-1892. 

26.  Duryea,  Edwin,   Jr.     Table  of  Excessive  Precipitation  of  Rain  at  Chi- 

cago,  Illinois,  from  1889  to  1897,  inclusive.     Jour.  W.   Soc.  of 
Engrs.    Feb.,  1899. 

CAUSES    OF   RAINFALL. 

27.  Henry,  D.  F.     Rainfall  with  Different  Winds.     Rept.  Chf.  Engr.  U.  S.  A. 

1867,  p.  598. 

28.  Blanford,  H.  F.     How  Rain  is  Formed.     Smithsonian  Report.     1889,  pt. 

1,  p.  287. 


132  Rainfall. 

29    Belschow,  Frantz  A.     The  Causes  of  Rain  and  the  Structure  of  the  At- 
mosphere.    Trans.  Am.  Soc.  C.  E.     Vol.  23,  p.  303.     1890. 

30.  Davis,  W.  M.     The  Causes  of  Rainfall.     Journal  of  N.  E.  W.  Wks.  Ass'n. 

1901. 

31.  Curtis,  G-.  E.    The  Effect  of  Wind  Currents  on  the  Rainfall.    Signal  Serv- 

ice Notes  No.  16. 

THE   EFFECT   OF   ALTITUDE    ON   RAINFALL. 

32.  Homersham,  S.  C.    Variations  of  the  Rainfall  with  the  Elevation.     Proc. 

Inst.  C.  E.,  Vol.  7,  pp.  276,  282  &  284.     1848. 

MEASUREMENT    OF    RAINFALL. 

33.  Clutterbuck,  J.  C.     Dalton's  Rain-gage.     Proc.  Inst.  C.  E.,  Vol.  9,  p.  157. 

1850. 

34.  Fitzgerald,  Desmond.     Does  the  Wind  Cause  the  Diminished  Amount  of 

Rain  Collected  in  Elevated  Rain  Gages?    Jour.  As  so.  of  Eng.  Soc. 
1884. 

35.  Weston,  E.  B.     The  Practical  Value  of  Self-recording  Rain-gages.     Eng. 

News,  1889,  Vol.  21,  p.  399. 

36.  Self-Registering  Rain-gages  and  Their  Use  for  Recording  Excessive  Rain- 

falls.   Eng.  Rec.  1891,  Vol.  23,  p.  74. 

37.  Duryea,  Edwin,  Jr.     Effect  of  Wind  Currents   on  Rainfall   and   on  the 

Gage  Record.     Signal  Service  Notes  No.  16. 


CHAPTER  VII. 

THE  DISPOSAL  OF  THE  RAINFALL. 

78.  Factors  of  Disposal. — The  portion  of  the  rainfall  in  which 
the  water  power  engineer  is  most  directly  interested  is  that  which 
runs  off  in  the  surface  flow  or  flow  of  streams.     In  order  to  form 
some  idea  of  the  amount  of  this  run-off  and  the  factors  that  control 
it,  it  is  necessary,  however,  to  investigate  and  consider  the  various 
ways  in  which  the  rainfall  is  distributed,  for  the  ways  in  which  the 
distribution  occurs  are  mutually  inter-dependent  and  of  necessity 
modify  and  control  each  other.    The  rainfall  disposal  depends  on  a 
large  number  of  factors  or  conditions  among  the  most  important 
of  which  may  be  named : 

(1)  The  amount  of  the  rainfall. 

(2)  The  rate  of  rainfall. 

(3)  The   condition   of  the   surface   on   which   the   rainfall   takes 
place. 

(4)  The  condition  of  the  underlying  geological  strata. 

(5)  The  atmospheric  temperature. 

(6)  The  direction  and  velocity  of  the  wind. 

(7)  The  nature  and  extent  of  vegetation. 

(8)  The  surface  topography. 

(9)  The  evaporation. 

It  will  be  noted  that  some  of  the  factors  mentioned  above  tres- 
pass more  or  less  on  others  and  are  not  clearly  separable. 

79.  The  Rate  or  Intensity  of  Rainfall. — It  will  readily  be  recog- 
nized that  with  very  heavy  or  intense  rainfall  a  larger  percentage 
of  the  water  will  run  directly  into  the  streams  and  a  smaller  per- 
centage will  be  taken  up  by  the  strata  than  would  be  the  case  were 
the  rainfall  very  light.     In  very  light  rainfalls  there  is  no  run-off, 
the  water  being  either  taken  directly  into  the  strata  or  re-evaporated 
from  the  surface. 


134  Disposal  of  the  Rainfall. 

80.  Condition   of   Receiving   Surfaces   and    Geological   Strata. — 
Next  in   importance  in   modifying  the   disposal   of  rainfall   is   the 
condition  of  the  surface  on  which  the  rain  falls  and  of  the  under- 
lying geological  strata.     If  the  geological  strata  are  porus  in  na- 
ture and  comparatively  free  from  water  they  will  readily  receive 
and  transmit  the  rainfall  if  the  surface  is  in  proper  condition  to  re- 
ceive it.    The  condition  of  the  surface  itself  modifies  the  reception 
of  the  rainfall  in  a  very  marked  manner.    With  high  surface  slopes 
the  rainfall  may  be  large,  even  with  somewhat  porous  strata,  and 
yet  very  little  water  will  be  taken  up  by  the  strata.     With  low 
slopes  and  porus  strata  a  large  amount  of  water  will  be  received 
directly  by  the  surface  and  passed  into  the  ground  water  and  deep 
waters  of  underlying  geological  strata. 

The  temperature  has  an  important  influence  on  the  condition  of 
the  strata,  and  consequently  the  disposal  of  the  rainfall.  Strata 
otherwise  porous  but  with  saturated  and  frozen  surface  will  re- 
ceive and  retain  practically  no  water  and  the  consequence  is  that 
under  these  conditions  even  a  low  rainfall  may  produce  a  consider- 
able run-off  that  under  other  temperature  conditions  would  not 
occur. 

81.  Effects  of  Wind. — The  wind  has  a  marked  effect  on  evapora- 
tion and  consequently  on  the  quantity  of  rainfall  that  passes  away 
in  the  atmosphere.     The  average  velocity  of  the  wind  will  vary  in 
different  parts  of  the  United  States  from  three  to  seventeen  miles 
per  hour  and,  other  things  being  equal,  will  increase  evaporation  as 
such  average  velocity  increases. 

82.  Effects  of  Vegetation. — The  nature  and  extent  of  the  vege- 
tation on  a  surface  has  a  marked  effect  on  the  disposal  of  the  rain- 
fall.     Experiments   at   the   Wisconsin    Agricultural    Experimental 
Station  show  that  barley,  oats  and  corn  require  15.2,  19.6  and  26.4 
inches  of  rainfall,   respectively,   to  produce  a  crop.     This  includes 
the  transpiration  and  evaporation  from  the  cultivated  surface  as 
well  as  the  actual  quantity  used  by  vegetation.     The  amount  act- 
ually retained  as  a  part  of  the  vegetable  growth  is,  of  course,  very 
small.    The  water  simply  serves  to  convey  the  soluble. foods  of  the 
soil   to   the   various   fibres   of   the   plant.     The   actual   amount   of 
water   used    in    irrigation    is    not   a    fair    criterion    of   the    amount 
needed  for  the  development  of  plant  life  as  in  most  cases  crops 
are   over-irrigated.     The   actual   depth   and   the   rainfall   and   irri- 
gation  water  used   on   crops   vary  from   as   low   as    12   inches   to 
sometimes  as  high  as   16  feet,  frequently  running  into   quantities 


Effects  of  Vegetation. 


135 


much  in  excess  of  any  ordinary  rainfall  in  moist  climates  where 
irrigation  is  found  to  be  unnecessary. 

In  the  Report  of  the  Kansas  State  Board  of  Agriculture  for  De- 
cember 31,  1889,  Mr.  W.  Tweeddale,  C.  E.,  gives  the  following  ta- 
ble containing  the  results  of  investigations  by  M.  E.  Risler,  a  Swiss 
observer,  upon  the  daily  consumption  of  water  by  different  kinds 
of  crops: 

TABLE.  X 
Daily  Consumption  of  Water  by  Crops. 


INCHES  01 

p  WATER. 

Minimum. 

Maximum. 

Lucern  grass  

0  134 

0  267 

IVIeadovv  2rrasc 

0  1" 

0  ''87 

Oats  

0.140 

0  193 

Indian  Corn 

0  110 

1  570 

Clover 

0  140 

Vinevard.                                                   ...       

0  035 

0  031 

Wheat                                                

0  106 

0  110 

Rye              .  .                  .     .                               .     .             

0  091 

Potatoes                                 

0  038 

0  055 

Oak  trees         .   .                  

0  030 

0.038 

Fir  Trees           

0.020 

0.043 

Mr.  Tweeddale  finds  that  this  table  agrees  with  careful  experi- 
ments made  in  France  and  elsewhere,  and  calculates  from  it  that 
from  seed  time  to  harvest  cereals  will  take  up  15  inches  of  water 
and  grass  may  absorb  as  much  as  37  inches. 

This  table  shows  also  one  of  the  important  reasons  why  a  de- 
crease of  stream  flow  follows  the  destruction  of  forests  and  their 
replacement  by  meadows  and  cultivated  fields.  It  is  quite  evident 
also  that  if  the  watersheds  were  covered  by  grasses  or  cereals  there 
would  be  comparatively  little  water  left  for  the  flow  of  streams. 
From  this  it  will  be  seen  that  the  character  of  the  vegetation  on  a 
watershed  exerts  a  considerable  influence  on  the  ultimate  distribu- 
tion of  the  rainfall. 

The  presence  or  absence  of  forests  has  also,  as  shown  by  a  series 
of  observations  in  Germany,  a  marked  effect  on  evaporation.  Prof. 
M.  W.  Harrington  (see  Bulletin  No.  7,  U.  S.  Dept.  of  Agriculture, 
p.  97)  has  compiled  the  accompanying  diagram  (Fig.  68),  which 
illustrates  clearly  the  effect  of  forests  upon  the  monthly  evapora- 
tion. The  upper  curve  represents  the  evaporation  from  water  sur- 


136 


Disposal  of  the  Rainfall. 


faces  in  the  open  country,  while  the  lower  curve  shows  the  evap- 
oration from  water  surfaces  in  the  woods.  The  shaded  area  thus 
illustrates  the  saving  due  to  the  cover  and  protection  of  forests. 

83.  Percolation. — On  pervious  and  unsaturated  strata  a  portion 
of  the  rainfall  sinks  below  the  surface  until  it  reaches  a  saturated 


Fig.  68. — Reduction  in  Evaporation  Due  to  the  Presence  of  Forests. 

or  a  relatively  impervious  stratum.  The  water  then  follows  the  dip 
of  the  stratum  until  it  reaches  an  outlet  along  some  stream  or  ap- 
pears in  the  form  of  springs,  frequently  in  an  entirely  different 
drainage  area  or  possibly  below  the  level  of  the  sea  itself.  It  is 
this  ground  water  that  gives  rise  to  the  dry  weather  flow  of 
streams,  and  frequently  is  the  only  source  from  which  stream  flow 
is  maintained  during  the  dry  seasons  of  the  year.  The  same  sources 
irequently  maintain  the  winter  flow  at  times  when  the  rainfall  is 
stored  on  the  watershed  in  the  form  of  snow  and  ice. 

Percolation  is  an  important  factor  in  the  storage-  of  water  and 
in  the  construction  of  raceways  and  canals  and  needs  most  careful 
attention  when  such  works  are  under  contemplation. 

A  large  amount  of  valuable  data  concerning  the  losses  due  both 
to  evaporation  and  seepage  has  been  collected  by  Mr.  E.  Kuichling 
in  connection  with  the  study  of  the  water  supply  for  the  New 
York  Barge  Canal  and  is  reproduced  in  the  Appendix. 

A  small  portion  of  the  ground  water  is  taken  up  by  the  roots  of 
plants  and  frequently  feeds  vegetation  during  dry  periods.  Water 
drawn  from  the  soil  for  such  purposes,  after  fulfilling  its  functions 
in  vegetation,  is  transpired  from  the  vegetable  surfaces  into  the 
atmosphere.  Streams  fed  from  areas  where  large  deposits  of  fine 
grained  but  porous  material  are  developed,  are  usually  more 
constant  in  flow  and  less  subject  to  fluctuations  either  from 
flood  or  drought.  The  flows  of  the  deeper  strata  usually  pass  far 
from  the  watershed  on  which  the  rainfall  occurs  and  modify  to  a 
limited  extent  the  stream  flow  in  other  valleys  frequently  far  from 
the  original  rainfall  source. 


Evaporation.  137 

84.  Evaporation. — Evaporation  takes  place  from  moist  surfaces 
and  from  the  water  surfaces  of  swamps,  lakes,  streams  and  the 
oceans,  whenever  such  surfaces  are  in  contact  with  unsaturated 
atmosphere.  The  absorption  of  the  rainfall  by  the  strata  effectively 
limits  the  amount  of  evaporation  from  a  given  area  by  reducing 
the  area  of  contact  of  wet  surface  with  the  atmosphere,  thus  con- 
fining the  evaporation  largely  to  free  water  surfaces.  Fig.  69 
shows  a  map  of  the  approximate  annual  evaporation  which  takes 
place  from  water  surfaces  at  various  points  within  the  United 
States.  It  will  be  noted  that  this  map  shows,  in  the  greater  por- 
tion of  the  United  States,  evaporations  equal  to  or  greater  than 
the  annual  rainfall  at  such  localities.  The  total  annual  evaporation, 
as  shown  in  the  map,  is  based,  however,  on  free  water  surfaces 
only,  and  evaporation  from  ground  surfaces  only  takes  place  from 
occasional  moist  surfaces  which  occur  after  rains  and  when  the 
humidity  is  high.  The  total  amount  of  water  evaporated,  there- 
fore, is  very  much  less  than  that  which  the  map  would  seem  to  in- 
dicate. This  map  and  the  table  of  monthly  evaporation  in  the 
appendix  are  taken  from  data  given  in  the  Monthly  Weather 
Review  of  September,  1888.  The  Weather  Review  observations 
are  not  based  on  absolute  evaporation  tests  but  are  deduced  from 
readings  of  dry  and  wet  bulb  thermometers  as  observed  at  various 
Signal  Service  Stations  in  1887  and  1888.  These  deductions  are 
supplemented  by  observations  at  several  stations  by  means  of  the 
Piche  evaprometer.  While  evaporation,  like  rainfall,  varies  from 
year  to  year  in  accordance  with  the  variation  in  the  controlling 
factors,  yet  in  lieu  of  more  extended  observations  this  map  and 
table  indicate  relative  conditions  at  the  various  stations  and  ap- 
proximately the  evaporation  from  free  water  surfaces.  The  com- 
parative monthly  evaporation  at  sixteen  stations  distributed 
throughout  the  United  States  is  shown  graphically  by  Fig.  70.  At  a 
number  of  Eastern  points,  namely,  Boston,  Rochester  and  New 
York,  evaporation  observations  have  been  made  for  a  number  of 
years  and  from  the  data  thus  collected  a  knowledge  of  the  local 
variations  that  occur  in  evaporation  at  these  points  can  be  obtained. 

Evaporation  is  greatly  promoted  by  atmospheric  currents  which 
have  perhaps  the  most  marked  effect  of  any  single  influence.  The 
temperature  of  the  water  and  the  humidity  of  the  atmosphere  also 
have  a  marked  effect.  Mr.  Desmond  Fitzgerald  in  a  paper  on 
evaporation  (see  Trans.  Am.  Soc.  C.  E.,  Vol.  XV,  page  581)  offers 
the  following  formula  for  evaporation : 


izr     las*     123'     icr     no*     nriM*     nr     nr     100*     lor     wy    toy     ior     99 


ii9c          lit"         115°          H3'          nr          109°          loT5         ios5          103°         101 


ANNUAL 
EVAPORATION' 

IN  THE 
UNITED  STATES 


140 


Disposal  of  the  Rainfall, 


No.  Atlantic,  So.  .Atlantic,  Gt.  Lawrence,  Ohio  River, 

New  Haven,  Conn.  Augusta,  Ga.  Detroit,  Mich.  Cincinnati,  O. 


-B 


Eastern  Gulf,  Western  Gulf, 

Montgomerj*,  Ala.          Palestine,  Tex. 


Upper  Mississippi,        Lower  Mississippi, 
Des  Moines,  la.  Little  Rock,  Ark. 


Missouri  River, 
Topeka,  Kans.  Helena,  Mont. 


Red  River, 
Moorehead,  Minn. 


No.  Pacific. 
Olympia,  Wash. 


Columbia, 
Spokane,  Wash. 


Pacific, 
Sacramento,  Cal. 


Colorado, 
Yuma,  Ariz. 


Great  Basin, 
Winnemucca,  Nev, 


Fig.  70. — Monthly  Evaporation  From  Free  Water  Surfaces  at  Various  Points 

in  the  United  States. 


Evaporation.  141 

E=(V-v)(1--r) 
60 

In  this  formula  V  equals  the  maximum  force  of  vapor  in  inches 
of  mercury  corresponding  to  the  temperature  of  the  water;  v,  the 
force  of  the  vapor  present  in  the  air;  W,  velocity  of  the  wind  in 
miles  per  hour;  and  E  the  evaporation  in  inches  of  depth  per  hour. 
The  value  of  v  depends  on  certain  relations  between  the  tempera- 
ture of  the  air  and  the  water.  From  a  careful  examination  of  the 
formula  it  will  be  seen  that  evaporation  as  represented  thereby  does 
not  depend  largely  on  temperature. 

Table  XI  is  taken  from  a  paper  on  "Rainfall,  Flow  of  Stream,  and 
Storage"  by  Mr.  Desmond  Fitzgerald  (Trans.  Am.  Soc.  C.  E.,  Vol. 
XXVII,  No.  3),  and  shows  the  monthly  evaporation  from  water 
•surface  at  Boston,  Massachusetts,  for  sixteen  years.  The  table  is 
partially  made  up  from  a  diagram  of  mean  monthly  evaporation  but 
•only  when  the  observation  practically  agreed  with  the  same. 

85.  Evaporation  Relations. — Professor  Cleveland  Abbe  gives  the 
following  relations  of  evaporation,  as  established'  by  Professor 
Thomas  Tate : 

(a)  Other   things   being   the    same,   the.   rate   of   evaporation   is 
nearly  proportional  to  the  difference  of  the  temperature  indicated 
by  the  wet-bulb  and  dry-bulb  thermometers. 

(b)  Other  things  being  the  same,  the  augmentation  of  evapora- 
tion due  to  air  in  motion  is  nearly  proportional  to  the  velocity  of 
the  wind. 

(c)  Other  things  being  the  same,  the  evaporation  is  nearly  in- 
versely proportional  tt>  the  pressure  of  the  atmosphere. 

(d)  The  rate  of  evaporation  of  moisture  from  damp,  porous  sub- 
stances of  the  same  material  is  proportional  to  the  extent  of  the 
surface  presented  to  the  air,  without  regard  to  the  relative  thickness 
of  the  substances. 

(e)  The  rate   of   evaporation   from   different   substances   mainly 
depends  upon  the  roughness  of,  or  inequalities  on,  their  surfaces, 
the  evaporation  going  on  most  rapidly  from  the  roughest  or  most 
uneven  surfaces ;  in  fact,  the  best  radiators  are  the  best  evaporizers 
of  moisture. 

(f)  The  evaporation  from  equal  surfaces  composed  of  the  same 
material  is  the  same,  or  very  nearly  the  same,  in  a  quiescent  at- 
mosphere, whatever  may  be  the  inclination  of  the  surfaces ;  thus  a 


1 42 


Disposal  of  the  Rainfall. 


".COO?"-C<lCiC^lOC 
CO  CC  C^J  1C  •«*!  -,£  t>-  C: 


C  GC  CO  GC  •—  i 


O  —  r-  ( 

*  *  * 


c:  O  c-  i^  co  Ci  »c  cc  c:  c^i  t^  io 

o  I-H  — i  :M  co  10  xc  ic  co  co  :M  r- 1 


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Evaporative  Relations.  143 

horizontal  plate  with  its  damp  face  upward  evaporates  as  much  as 
one  with  its  damp  face  downward. 

(g)  The  rate  of  evaporation  from  a  damp  surface  (namely,  a 
horizontal  surface  facing  upward)  is  very  much  affected  by  the 
elevation  at  which  the  surface  is  placed  above  the  ground. 

(h)  The  rate  of  evaporation  is  affected  by  the  radiation  of  sur- 
rounding bodies. 

(i)  The  diffusion  of  vapor  from  a  damp  surface  through  a 
variable  column  of  air  varies  (approximately)  in  the  inverse  ratio 
of  the  depth  of  the  column,  the  temperature  being  constant. 

(j)  The  amount  of  vapor  diffused  varies  directly  as  the  tension 
of  the  vapor  at  a  given  temperature,  and  inversely  as  the  depth  of 
the  column  of  air  through  which  the  vapor  has  to  pass. 

(k)  The  time  in  which  a  given  volume  of  dry  air  becomes  satu- 
rated with  vapor,  or  saturated  within  a  given  percentage,  is  nearly 
independent  of  the  temperature  if  the  source  of  vapor  is  constant. 

(i)  The  times  in  which  different  volumes  of  dry  air  becon  e 
saturated  with  watery  vapor,  or  saturated  within  a  given  per  cent, 
are  nearly  proportional  to  the  volumes. 

(m)  The  vapor  already  formed  diffuses  itself  in  the  atmosphere 
much  more  rapidly  than  it  is  formed  from  .the  surface  of  the  water. 
(This  assumes,  of  course,  that  there  are  no  convection  currents  of 
air  to  affect  the  evaporation  or  the  diffusion.) 

86.  Practical  Consideration  of  Losses. — From  the  previous  dis- 
cussion it  will  be  readily  realized  that  it  would  be  impossible  to  dif- 
ferentiate all  of  the  methods  of  the  disposal  of  rainfall  upon  a  drain- 
age area.  Evaporation  differs  widely  from  different  classes  of  vege- 
tation and  from  different  classes  of  land  surfaces ;  also  on  account 
of  the  slope  and  exposure.  No  two  square  miles  upon  a  drainage 
area  offer  the  same  conditions  as  affecting  evaporation  which  differs 
very  widely  with  such  conditions.  Evaporation  and  seepage  from 
any  surface  varies  with  the  temperature,  with  the  moisture  in  the 
air,  and  with  the  velocity  of  the  wind.  It  is  therefore  impossible 
to  compute,  with  any  degree  of  accuracy,  evaporation  over  an  ex- 
tended surface  of  a  watershed  or  drainage  area,  or  to  ascertain 
with  any  degree  of  accuracy  the  probable  losses  that  will  take  place 
in  the  same  area. 

For  water  power  purposes,  the  rainfall  can,  therefore,  be  divided 
into  two  quantities  in  which  the  water  power  engineer  is  interested : 
First :  The  run-off  on  which  the  power  developed  directly  depends, 


OF  THE 


144  Disposal  of  the  Rainfall. 

and,  Second :  The  losses,  by  whatever  means  they  occur,  which  are 
not  available  for  such  purposes.  Evaporation  is  usually  but  not 
always  the  source  of  greatest  loss  on  a  drainage  area  and  commonly 
other  sources  of  loss  are  insignificant  when  compared  with  it.  It  is 
therefore  a  common  practice  to  deduct  the  run-off  from  the  rainfall 
on  a  given  drainage  area  and  to  classify  the  difference  as  evapora- 
tion, including  under  this  term  all  losses  of  this  same  general 
character,  whether  through  seepage,  evaporation  or  otherwise. 

LITERATURE. 

1.  Vermeule,  C.  C.    Report  on  Water  Supply.     Geol.  Survey  of  New  Jersey. 

Vol.  III.    1894. 

2.  Vermeule,  C.  C.    Report  on  Forests.     Geol.  Survey  of  New  Jersey.     1899. 

3.  Turneaure  and  Russell.     Public  Water  Supplies,   Chap.  V.     New  York,. 

Wiley  &  Sons.    1901. 

4.  Rafter,  George.     Hydrology  of  the  State  of  New  York.     pp.  4G-197.     Al- 

bany, N.  Y.     New  York  State  Education  Dept.  Bui.  85,  1905. 

PERCOLATION. 

5.  Lawes,  J.  B.     The  amount  and  Composition  of  the  Rain  and  Drainage 

Waters   Collected  at  Rothamsted.     Jour.   Royal  Agric.    Soc.   of 
England,  Vol.  17,  p.  241,  1881;  Vol.  18,  p.  1,  1882. 

€.  Fortier,  Samuel.  Preliminary  Report  on  Seepage  Wiater,  and  The  Un- 
derflow of  Rivers.  Bulletin  No.  38,  Agric.  Expt.  Station,  Logan, 
Utah.  1895. 

7.  Seepage    or    Return    Waters    from    Irrigation,    Bulletin    No.    33.      Colo. 

Agric.  Expt.  Sta.,  Fort  Collins,  Colorado.     1896. 

8.  Fortier,  Samuel.     Seepage  Water  of  Northern  Utah.     Water  Supply  and 

Irrigation  Paper  No.  7.     1897. 

9.  The  Loss  of  Water  from  Reservoirs  by  Seepage  and.  Evaporation.     Bul- 

letin No.   45.     Colo.   Agric.   Expt.    Sta.,   Fort  Collins,   Colorado. 
May,  1898. 

10.  Loss  from  Canals  from  Filtration  or  Seepage.     Bulletin  No.   48.     Colo. 

Agric.  Expt.  Sta.,  Fort  Collins,  Colorado.     1898. 

11.  Kuichling,  Emil.     Loss  of  Water  from  Various  Canals  by  Seepage.     (See 

paper  on  Water  Supply  for  New  York  State  Canals,  Report  of 
State  Engineer  on  Barge  Canal,  1901). 

12.  Wilson,  H.  M.     Irrigation  Engineering.     New  York,  Wiley  &  Sons.    1903. 

13.  Wilson,  H.  M.     Irrigation  in  India.     Water  Supply  and  Irrigation  Paper 

No.  87.     1903. 

14.  Mead,  D.  W.    Report  on  Water  Power  of  the  Rock  River.    Chicago.    Pub. 

by  the  author.     1904. 

EVAPORATION. 

15.  Greaves,  Charles.     On  Evaporation  and  on  Percolation.     Proc.  Inst.  C.  E. 

1875-76.     Vol.  45,  p.  19. 


Literature.  145 

16.  Fitzgerald.  Desmond.     Evaporation.     Trans.  Am.   Soc.  C.  E.,  Vol.  15,  p. 

581.     Sept.,  188G. 

17.  Loss   of  Water  from  Reservoirs  by   Seepage  and   Evaporation,   Bulletin 

No.  45,  Colo.  Agric.  Expt,  Sta.,  Fort  Collins,  Colo.     May,  1898. 

18.  Depth  of  Evaporation  in  the  United  States.     Monthly  Weather  Review. 

September,  1888. 

19.  Depth  of  Evaporation  in  the  United  States,  Engineering  News,  Decem- 

ber 30th,  1888;  January  5th,  1889. 

20.  Harrison,  J.  T.     On  the  Subterranean  Water  in  the  Chalk  Formation  of 

the  Upper  Thames  and  its  Relation  to  the  Supply  of  London. 
Proc.  Inst.  C.  E.     1890-91.     Vol.  105,  p.  2. 

21.  Fernow,  B.  E.     Relation  of  Evaporation  to  Forests.     Bulletin  No.  7,  For- 

estry Div.,  U.  S.  Dept.  Asric.  and  Engineering  News,  1893,  Vol. 
30,  p.  239. 

22.  Kimball,  H.  H.     Evaporation  Observations  in  the  United  States.     Read 

before  the   Twelfth   National   Irrigation   Congress,   1904;    Engi- 
neering News,  April  6,  1905. 

USE    OF    WATER    IN    AGRICULTURE. 

The  Publications  of  the  United  States  Experiment  Stations  on  Irriga- 
tion and  of  the  Experiment  Stations  of  the  various  States  contain  much 
information  on  this  subject.  The  following  are  of  especial  importance: 

23.  Hill,  W.  H.     Report  of  State  Engineer  to  Legislature  of  California,     2 

Vols.     Sacramento,  1880. 

24.  Carpenter,  L.  G.     Duty  of  Water.     Bui.  22, 'Agric.  Expt.  Sta.,  Fort  Col- 

lins, Colorado.     1893. 

25.  Fortier,  Samuel.     Water  for  Irrigation.     Bui.  26,  Utah  Agric.  Expt.  Sta., 

Logan,  Utah.     1893. 

26.  Report  of  Irrigation  Investigations,  U.   S.  Dept.  Agriculture,  Irrigation 

Inquiry.     Bui.  86  for  the  year  1899. 

27.  King,  F.  H.     Irrigation  and  Drainage.     New  York.     MacMillan  Co.,  1902. 

The  amount  of  Water  Used  by  Plants,  pp.  16-46.    Duty  of  Water, 
pp.  196-221. 

28.  Mead,  Elwood,     Irrigation  Institutions,  Chap.  VII,  The  Duty  of  Water. 

New  York.    MacMillan  Co.    1903. 

29.  Wilson,  H.  M.     Irrigation  Engineering,  Chap.  V.,  Quantity  of  Water  Re- 

.quired.    New  York,  Wiley  &  Sons.    1903. 


CHAPTER  VIII. 

RUN-OFF. 

87.  Run-Off. — That  portion  of  the  rainfall  that  is  not  absorbed 
by  the  strata,  utilized  by  vegetation  or  lost  by  evaporation,  finds 
its  way  into  streams  as  surface  flow  or  run-off.  The  demands  of 
the  first  named  factors  are  always  first  supplied  and  the  run-off  is 
therefore  the  overflow  or  excess  not  needed  to  supply  the  other 
demands  on  the  rainfall.  The  run-off,  therefore,  while  a  direct  func- 
tion of  the  rainfall,  is  not  found  to  increase  in  direct  proportion 
thereto,  except  perhaps  in  seasons  such  as  early  spring  when  from 
seasonal  conditions  the  demands  of  vegetation,  percolation  and 
evaporation  are  not  active  and  all  or  most  all  of  the  rainfall  flows 
away  on  the  surface.  The  remainder  of  the  year  the  run-off  may 
be  said  to  increase  with  the  rainfall  but  usually  at  a  much  less 
rapid  rate  and  in  many  cases  the  rainfall  is  entirely  absorbed  by 
the  strata  or  vegetation,  and  does  not  influence  or  affect  the  run-off. 
In  this  case  the  run-off  is  supplied  from  the  ground  water,  stored 
from  previous  rainfalls,  and  is  entirely  or  largely  independent  of 
the  immediate  rainfall  conditions. 

An  examination  of  the  observed  run-off  of  streams,  and  the  rain- 
fall on  their  respective  drainage  areas,  for  annual,  monthly  and  sea- 
sonal periods,  will  show  that  there  is  a  relation  more  or  less  direct 
between  the  rainfall  and  run-off  (see  Fig.  71,  et  seq.).  The  relations 
are  shown  by  various  diagrams  and  mean  curves  from  which  many 
departures  will  be  noted.  The  departure  of  individual  observations 
from  the  mean  curve  expressing  these  relations  shows  the  relative 
importance  and  influence  of  other  factors  in  affecting  such  relations. 
The  relations  of  the  numerous  factors  which  are  known  to  influence 
the  results  are  quite  complex  and  are  not  well  established  and  much 
more  meteorological  information  in  much  greater  detail  and  a  care- 
ful consideration  and  study  of  the  same  will  be  necessary  before 
such  relations  can  be  even  approximately  established. 


Run-Off. 


147 


148  Run-Off. 

88.  Influence  of  Various  Factors. — The  influence  of  various 
factors  of  disposal  was  discussed  in  the  last  chapter.  Evaporation 
is  known  to  vary  with  temperature,  the  direction  and  velocity  of 
the  winds,  barometric  pressure,  and  various  other  meteorological 
influences,  and  yet  no  clearly  defined  relation  has  yet  been  shown 
to  exist  between  these  factors,  by  means  of  which  their  actual  in- 
fluence on  the  run-off  can  be  approximately  calculated.  Mr.  C.  C. 
Vermeule  (see  Vol.  Ill,  Geol.  Survey  of  New  Jersey)  considers 
that  annual  evaporation  depends  largely  on  the  mean  annual  tem- 
perature #nd  offers  a  formula  for  the  calculation  of  the  same,  which,, 
in  many  cases,  gives  results  which  seem  to  agree  closely  with  the 
facts  and  data  collected  from  a  number  of  Eastern  drainage  areas. 
Mr.  Vermeule'' s  formula  for  the  relation  between  annual  evaporation 
and  precipitation  on  the  Passaic  River,  and  some  other  Eastern 
drainage  areas  where  conditions  are  similar,  is : 

E=  15-50+0.16  R 
in  which 

E=The  annual  evaporation  (including  all  losses  on  drainage  area: 
except  from  run-off) 

and  R=the  annual  rainfall. 

For  general  application  to  all  streams  he  suggests  the  formula 

£=(15.50+0.16  R)   (0.05  T— 1.48) 
in  which  T=  mean  annual  temperature. 

Mr.  Vermeule  also  offers  a  formula  for  the  evaporation  for  each 
month  and  discusses  at  length  the  influence  of  ground  storage  on 
the  flow  of  streams.  Mr.  Geo.  W.  Rafter  (see  Water  Supply  and 
Irrigation  Paper  No.  80)  has  made  a  careful  analysis  of  available 
data  which  indicates  that  no  such  intimate  relation  can  be  found  to 
exist.  In  general,  the  information  available  does  not  seem  to  show 
that  other  factors  have  a  sufficiently  definite  relation  to  run-off  or 
to  each  other  to  make  such  relation  clearly  manifest  and  yet  such 
factors  are  known  to  have  an  unmistakable  and  constant  influence. 
This  fact  is  quite  clearly  demonstrated  by  a  number  of  diagrams 
prepared  by  Mr.  Rafter,  which  are  here  reproduced. 

Figure  72  shows  graphically  the  relation  between  precipitation, 
evaporation,  run-off  and  temperature  on  the  Lake  Cochituate  basin 
for  thirty-three  years.  In  this  diagram  the  years  are  arranged  in 
accordance  with  the  precipitation.  In  a  general  way  the  evapora- 
tion and  run-off  for  these  years  may  be  said  to  vary  with  the  pre- 


Influence  of  Various  Factors. 


149 


co 


O> 

* 


15 


4J  50° 

*53 

c  4P° 

£ 

•§  450 

£  ^7° 


Years 


Years  arranged  in  order  of  dryness. 

Fig.  72.  —  Relation  Between  Precipitation,  Evaporation,  Run-off  and  Tempera- 

ture on  Lake  Cochituate  Basin. 
9 


Run-Off. 


cipitation.  Evaporation,  which,  it  must  be  remembered,  here  in- 
cludes all  losses  except  that  due  to  run-off,  increases  in  general 
as  the  rainfall  on  the  area  increases  and  decreases  with  the  rainfall, 
For  limited  periods,  however,  this  general  law  does  not  hold. 
Other  factors  affect  the  relations  and  cause  material  departures 
from  the  general  law.  This  is  particularly  marked  in  the  years  1891 
and  1872.  For  these  two  years  the  rainfall  was  almost  identical  in 
amount.  The  evaporation  for  the  same  years,  however,  differed 
materially,  being  about  16  inches  greater  in  1891  than  in  1872.  As 
a  consequence  the  run-off  for  the  year  1891  was  about  15%  inches 
greater  than  in  1872. 

In  order  to  demonstrate  the  mutual  relation  between  evaporation 
and  temperature  the  data  illustrated  in  the  previous  figure  has  been 


60° 
49° 
48° 
47° 
46° 


44° 


50 


40 


30 


1G 


i/ 
Years 


Fig.  73.—  Relation  Between  Evaporation  and  Temperature  on  Lake  Cochituate 

Basin. 

Years  being  arranged  according  to  amount  of  evaporation. 


Influence  of  Various  Factors. 


.  74 -Relations  between  reen- 
tat,on,  Run.0ff,  Evaporation  and 
Temperatnre  on  Sudbllry 


^ss&sas*** 

ration  respectively.  'g  eVap°- 


129"     lay     125"     i23»     «r     119°     nr     us*    113°    ur     109*     lor    105°    103*    ior     99' 


47 


05°       93°        91*         89°       flr  '      85"        83°         81°          79'         11'         IS* 


cy      er       65° 


OP  THE 

UNITfcDJSTATES 


154 


Run-Off. 


60 


40 


30 


20 


JO 


44° 


- 


40° 


20 


10 


Vo/irc 

Years 


30 


20 


10 


44° 
•439 
42° 
41° 
40° 


YEAXS* 


Fis  75—Relations  Between  Precipitation,  Run-Off,  Evaporation  and  Tempera- 
ture on  Upper  Hudson  River. 
Years  arranged  according  to  regular  order  and  decreasing  evaporation. 

rearranged  by  Mr.  Rafter,  and  in  Figure  73  the  relation  for  the 
years  has  been  arranged  in  the  order  of  their  evaporation,  and  com- 
pared with  the  mean  temperature  for  the  year.  This  figure  serves 
to  show  that  while  temperature  may,  and  unquestionably  docs, 
influence  evaporation,  yet  the  mean  annual  temperature  has  no 
controlling  effect  on  the  annual  evaporation.  It  will  be  noted  that 
for  the  year  1878,  when  the  mean  temperature  was  a  maximum,  the 
evaporation  was  considerably  below  the  average  for  this  drainage 


Relations  of  Annual  Rainfall  and  Run-Off. 


155 


area.  Similar  relations  for  the  Sudbury  River  basin  are  shown  in 
Fig.  74  and  for  the  Upper  Hudson  River  basin  in  Fig.  75. 

89.  Relations  of  Annual  Rainfall  and  Run-Off. — Figure  76  is  a 
mean  run-off  map  of  the  United  States  and  should  be  compared 
with  the  map  of  average  rainfall.  The  run-off  as  shown  by  this  map 
is  expressed  in  inches  on  the  drainage  area  and  similarly  to  the  com- 
mon expression  for  the  amount  of  rainfall.  The  value  of  this  map 
is  comparative  only.  In  this  case,  as  in  the  cases  of  rainfall  and 
evaporation,  the  mean  conditions  are  subject  to  wide  variations. 
A  detailed  study  of  local  conditions  is  always  necessary  in  order 
to  fully  understand  and  appreciate  the  influence  of  extreme  condi- 
tions and  of  local  factors. 

The  relation  between  the  annual  rainfall  and  run-off  on  various 
drainage  areas  is  shown  in  Figures  71  to  75,  inclusive,  as  previously 
described.  The  mean  relations  between  these  two  factors  on  four 
selected  drainage  areas  are,  however,  more  clearly  shown  by  the 
graphical  diagrams  Figs.  77,  78  and  79.  From  these  diagrams  a 


Pig.  77. 


RUN-OFF  DIAGRAM    OF  HUDSON  MD    GENESEE   RIKRS 
.  HUDSON  RIVER,  teaa-iooi 

INCHES  ON  CATCHMENT  AREA 

PERIOD          HAXIMUM  YEAR  HINIHUM  YEAR  HEAR 

I  *..-<./.  fM»w  tahfalt.   ««»-«/.    ttatef  J5j 

2.45        li.7»       11. SI      4.11  20.1  16.1          4.5 

19.12         C.S7     12.2S        10.37         2.33       «.«>  12.7  3.S 

S.iO          3.71      S.09        10 Jt         3.4}       7.0i  10.}  3.7 

S3.S7        33.08     10.79       31.17        17.4*     IHJ1  4tJ          S3J 


of  Hudson  River  Indicate*  ikut  & 


iii 


INCHES  ON  CATCHIKNT  AREA 

YEAR    H/fHMUH  YEAR  0CM 


27.71  75.73  71. m  13.20  S.S3   7.57    11.4  li.S      «J 

cn*taf         7.95   ;.«  e.iiii.n  b.seto.77  11.9   1.7    *J 

*,i*.i,u.g.  li.it  lit  ».»4  jtCT  M«  ii»  ^1  *£    Id 

Total.               47.7*  I».U  1S.41  31.00  C.tf  H.33  10.3  lit  ,  MLI 


Prvipltatlon  In  tatefti  eateluntirt  *na 


\  \ 


Fig   78. 


156 


Run-Off. 


mean  relation  can  be  traced  for  each  area  from  which,  however, 
there  are  considerable  departures  in  individual  years.  The  study, 
therefore,  of  this  subject  on  this  basis  will  demonstrate  the  mean 
relation  and  the  departure  therefrom  which  must  be  expected  on 
the  area  considered  and  other  areas  where  physical  conditions  are 
similar. 


KUK-OFf   DIAGRAM    OF   MUSK/NGUM    RIVER 

1888-1895 
INCHES  OH  CATCHMENT  AREA 


HAXIMUM  YEAH 


HIHIHUH  YEAR  HEAM 

•Of.  CM**.      /tatnfaJl.  frn.of. 

I3.S4  4.04  g.OO 

S.14  0.4»  f.SS 

7.6t  OJ7  7.tt 

2S.»4  4JO 


•i    r—r~-(—r    i 

44  45  SO  SS  60  SS 


Fig.  79 


Table  'X.ll.—Muskingum  River,  1888-1895,  inclusive. 

[Catchment  area=5,828  square  miles.] 


1888. 

1889. 

- 

1890. 

Period. 

Rain- 
fall. 

Run- 
off. 

Evapo" 
ration- 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Storage  

17.16 

5.17 

11.99 

13.52 

6/02 

7  50 

27.77 

]8  07 

9  70 

Growing  
Replenishing  ........... 

14.31 
11.14 

1.77 
3.39 

12.54 
7.75 

12.12 
10.24 

1.24 
96 

10.88 
9  28 

13.68 
15  52 

2.64 
6  13 

11.04 
9  39 

Year       

42  61 

10  33 

32  28 

35  88 

8  22 

27  66 

56  97 

26  84 

30  13 

1891. 

1892. 

1893. 

Storage 

16  72 

12  42 

4  30 

20  39 

9  06 

11  33 

25  04 

14  13 

10  91 

Growing 

13  56 

1  77 

11  79 

16  54 

3  65 

12  89 

8  31 

1  22 

7  00 

Replenishing1 

7  08 

1  37 

5  71 

4  81 

67 

4  14 

9  01 

85 

8  16 

Year  

37.36 

15.56 

21.80 

41.74 

13.38 

28.36 

42.36 

16.20 

26.16 

1894. 

J895. 

Storage 

16  93 

7  63 

9  30 

13  04 

4  04 

fi  00 

Growing 

4  56 

OC 

3  90 

9  14 

49 

8  6£ 

Replenish  ing 

9  02 

.41 

8  61 

7  6<> 

37 

*729 

Year  

30.51 

8.70 

21.  el 

29.84 

4.90 

24.94 

.         J 

The  Water  Year.  157 

90.  The  Water  Year. — The  relation  of  annual  rainfall  and  annual 
run-off  is  more  or  less  obscured  by  variations  in  the  periodic  dis- 
tribution of  the  annual  rainfall.  A  study  of  the  relation  of  the 
periodic  rainfall  and  the  periodic  run-off  is  therefore  necessary. 

For  a  comprehensive  understanding  of  the  relation  of  rainfall  to 
run-off  it  is  more  convenient  to  refer  to  the  water  year  instead  of 
the  calendar  year.  The  water  year  is  the  annual  division  of  time 
that  represents  the  full  annual  cycle  of  change  in  hydrological 
conditions.  It  does  not,  as  a  rule,  conform  very  closely  to  the  calen- 
dar year,  neither  is  the  water  year  constant  for  each  annual  period 
in  its  beginning  or  end,  but  varies  as  meteorological  conditions 
vary. 

As  previously  stated,  in  the  greater  portion  of  the  United  States, 
the  water  year  naturally  divides  itself  into  periods,  beginning,  ap- 
proximately, with  December,  and  ending,  approximately,  with  the 
following  November.  The  period  from  December  to  and  including 
May  is  termed  the  "Storage"  period ;  June,  July  and  August  con- 
stitute the  "Growing"  period,  and  September,  October  and  Novem- 
ber are  termed  the  "Replenishing"  period.  Not  only  the  year  but 
these  periods  as  well  vary  each  year,  and  are  not  necessarily 
limited  by  our  artificial  division  of  calendar  months  and  years. 

During  the  storage  period,  the  snows  of  winter  and  the  rains  of 
spring  saturate  the  ground,  and  a  large  amount  of  water  is  held  in 
storage  in  lakes,  swamps,  and  forests,  and  in  pervious  soils,  sands 
and  gravels.  The  portions  of  this  stored  water  tributary  to  a  drain- 
age area  but  not  necessarily  within  the  boundaries  thereof,  and  at 
elevations  above  the  level  of  the  stream,  are,  when  conditions  de- 
mand, available  to  supply  the  stream  flow,  and  are  also  available 
for  the  purpose  of  sustaining  plant  life.  Such  waters  will  feed  a 
stream  to  an  extent  depending  on  their  character  and  magnitude, 
regardless  of  the  amount  of  the  immediate  rainfall,  and  will  cause  a 
stream  to  flow  for  several  months,  even  without  rain,  if  the  per- 
vious deposits  and  other  storage  resources  are  well  developed 
upon  the  area.  These  relations  vary  widely  with  each  individual 
area,  and  in  areas  not  well  provided  with  such  deposits  the  streams 
often  run  dry  through  the  warm  days  of  summer. 

Whenever  the  surface  of  the  stream  falls  below  the  ground  water 
gradient  the  ground  water  is  affected  and  begins  to  supply  the 
stream  flow.  This  sometimes  occurs  early  in  May,  and  seldom 
later  than  the  beginning  of  June.  During  June,  July  and  August 
the  rainfall  is  rarely  sufficient  to  take  care  of  the  evaporation  and 


Run-Off. 


growth  of  vegetation  without  something  of  a  draft  on  the  ground 
water,  and  the  stream  flow  during  this  period  is  usually  entirely 
dependent  on  the  ground  water,  except  during  exceptionally  heavy 
rainstorms.  By  the  end  of  the  growing  period  about  August  3ist 
the  ground  water  is  often  so  reduced  as  to  be  capable  of  storing 
several  inches  of  rainfall.  During  the  replenishing  and  storage 
periods  of  winter  and  spring  the  ground  begins  to  receive  its  store 
of  water,  and,  with  favorable  rainfalls,  the  ground  becomes  fully 
saturated  by  the  end  of  April  or  May. 

Ta,ble  XIII.—  Hudson  River,  1888-1901,  inclusive. 
[Catchment  area=4,500  square  miles.] 


1888. 

1889. 

1890. 

Period. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Storage           .......... 

20.40 

17.06 

3.34 

17.10 

14.04 

3.06 

24.75 

19.28 

6.47 

GrAwipg              -  -    .  ... 

10.25 

2.05 

8.20 

15.05 

4.28 

10.79 

13.50 

2.85 

10.65 

Replenishing            - 

13.27 

4.53 

8.74 

10.81 

3.41 

7.40 

12.10 

6.81 

5.29 

Year.               

43;  92 

a  23.  64 

20.28 

a42.96 

21.71 

21.25 

«50.35 

28.94 

21.41 

1891. 

1892. 

1893. 

Storage 

20  69 

IS  59 

4  10 

24  95 

22  50 

2  45 

19  83 

15  20 

4  63 

13  49 

2  07 

11  42 

19  12 

6  87 

12  25 

13  37 

3  12 

10  25 

Replenishing  

8.78 

1.90 

-   6.88 

9.80 

3.71- 

6.09 

8.98 

3.59 

5.39 

Year....,  

42.96 

20.56 

22.40 

'53.87 

33.08 

20.79 

42.18 

21.91 

20.27 

1894. 

1895. 

1896. 

Storage 

21.37 

13.18 

8.19 

15.79 

11.68 

4.11 

22  17 

18.52 

5  65 

Growing 

8.73 

3.20 

6.53 

10.37 

2.36 

8.01 

10  25 

2  53 

7  72 

Replenishing 

11  87 

2  99 

8.88 

10.51 

3.42 

7.09 

12  79 

4  58 

8  21 

Year 

41.97 

19  37 

22  60 

36  67 

17  46 

19  21 

45  21 

23  62 

21  58 

1897 

1898. 

1899. 

Storage  

19.77 

14.60 

5.17 

22.80 

18.61 

4.19 

19.48 

15.15 

4.3S 

Growing......  

15.80 

7.79 

8.01 

13.52 

8.24 

10.28 

7.40 

1.63 

6.77 

Replenishing  

10  94 

3.80 

7.14 

12.19 

5.27 

6.92 

8.91 

2.76 

6.15 

Year  

46  51 

26  19 

20.32 

48.51 

27.12 

21.39 

35.79 

19  54 

16.25 

1900. 

1901. 

Storage......  

21.13 

16.12 

5.01 

18.47 

14  84 

3  63 

Growing  

12.11 

2.30 

9.81v 

15.09 

4.02 

11  07 

ReptentflhiTi  g  

12.17 

2.25 

9.92 

9.02 

3 

6  02 

Year  

45  41 

20.67 

24.74 

42.58 

21.86 

20.72. 

i  Approximate. 


Relations  of  Periodic  Rainfall  to  Run-Off. 
Table  XIV.— Connecticut  River,  1872-1885,  inclusive. 

[Catchment  area =10,334  square  miles,  j 


159 


1872. 

1873.  a 

1874.  « 

Period. 

Rain- 
fall. 

Run-- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
fall. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

14.92 

13.30 

1.62 

18.18 

21.80 

3.64 

23.08 

23.04 

0.04 

18.96 

6.29 

12.67 

10.11 

2.71 

7.40 

14.37 

6.62' 

.  7  75 

12.42 

6.64 

5.78 

15.04 

5.22 

9.82 

7.76 

2.15 

5  61 

Year 

48.30 

26.23 

20.07 

43.31 

29.73 

13.58 

45.21 

81  81 

13  40 

Period 

1875. 

1876.  a 

1877. 

Storage                 

17.51 

15.-47 

2.04 

22.50 

24.74 

-  2.24 

18.09 

12.68 

5  41 

14.55 

3.80 

10.75 

12.51 

3.35 

9.16 

14.00 

2  91 

11  09 

Replenishing 

11  38 

3.60 

•     7.76 

10.57 

2.28 

8.29 

13  08 

5  27 

'   7  81 

Year 

43  42 

22.87 

20.55 

45.58 

30.37 

15.21 

45  17 

20  86 

24  81 

Period.                                      1878.                                     1879. 

1880; 

Storage 

21.88 
13.59 
10.58 

18.02 
3.45 
3.06 

3.86 
10.14 

7.50 

23.19 
18.07 

9.48 

21.49 
2.92 
2.93 

1.70 
13.15 
6.55 

18.29 
11.82 
11.58 

14.78 
2.45 
2.62 

3.51 
9.  S7 
8.96 

Replenishing  

Year  

46.03 

24.53 

21.50 

'  48.74 

27.34 

21.40 

41.69 

•19.85 

21.84 

Period. 

1881. 

1882. 

1883. 

Storage 

20.83 
11.30 
11.38 

16.02 
2.93 
3.39 

4.81 
8.37 
7.99 

&20.50 
611.45 
b6.  50 

12.14 
3.35 

2.17 

8.38 
8.10 
4.33 

ft  12.  65 
&13.50 
&6.20 

8.73 
2.51 
1.37 

4.12 
10.99 
•  4.88 

Growing  

Replenishing  

Year  

43.51 

22.34 

21.17 

38.45 

17.66 

20.79 

32.55 

12.61 

19.94 

Period. 

1884. 

1885. 

Storage 

21.42 
12.14- 
8.51 

20.20 
2.79 
2.61 

1.22 
9.35 
5.90 

18.58 
14.82 
11.76 

13.63 
3.20 
5.61 

4.85 
11.62 
6.15 

Growing 

Replenishing 

Year 

42.07 

25.60 

16.47 

45.16 

22.44 

22.72 

"Not  included  in  mean. 


b  Rainfall  computed,  approximate. 


91.  Relation  of  Periodic  Rainfall  to  Run-Off. — For  streams  where 
the  observations  of  flow  have  been  made  for  a  number  of  years, 
comparisons  can  readily  be  made  of  the  relation  of  annual  and 
periodic  rainfall  and  run-off.  Such  investigations  should  be  made 
by  the  water  power  engineer  when  considering  a  river  relative  to 
its  availability  for  water  power  purposes.  An  analysis  of  such 
data  for  the  Muskingum,  Hudson,  and  Connecticut  Rivers  as  made 
by  Mr.  Rafter,  is  shown  in  Tables  XII,  XIII  and  XIV  (for  ad- 


i6o 


Run-Off. 


ditional  tabular  data  see  Appendix).  Graphical  representations  of 
the  periodic  relations  of  the  rainfall  and  run-off  on  the  Upper 
Hudson  River  basin  are  shown  in  Fig.  80,  and  the  same  relations 
for  the  Sudbury  River  basin  are  shown  in  Fig.  81. 


9    , 
§    '0 
tf    ^ 


Storage  period 


25, 


SO, 


40 


80 


15  20 

Precipitation  in  inches 


25 


JO  15  20 

Precipitation  in  inches 


25 


30 


25 


30 


5  10  15  ?0 

Precioitatfon  in  Inches 

Fig.  80. — Rainfall  and  Run-Off  of  Upper  Hudson  River  for  Each  Period  of  the 

Water  Year. 


[From  W.  S.  and  I.  Paper  No.  80  "Relation  of  Rainfall  to  Run-Off.'  ] 


Relations  of  Periodic  Rainfall  and  Run-Off. 


161 


40 


20-= 


Qc 
10         10 


Storage  period 


30 


25 


JO  15  20  25 

Precipitation  in  inches 
10  15  20  25 


40 


30 


35 


30  S5 


10 


Crowing  period 


10  15 

Precipitation  in  Incites 
10  15  20 


25 


30 


20  20 

Replenishing  period 


10  $      70 


w 


15 


20 


Precipitation  in  inches 
10  15  20 


30 
30 


Fig.   81. — Rainfall  and  Run-Off  of   Sudbury  River  for  Each   Period   of  the 

Water  Year. 


[From  W.  S.  and  I.  Papar  No.  80  "Relation  of  Rainfall  to  Run-Off. "J 


1 62  Run-Off, 

92.  Monthly  Relation  of  Rainfall  and  Run-Off.— The  relations  of 
rainfall  to  run-off  from  month  to  month  on  a  given  drainage  area 
are  not  usually  as  direct  and  definite  as  the  annual  and  periodic  re- 
lations. The  mean  and  extreme  relations  can,  however,  often  be 
established  within  somewhat  wider  limits,  and  such  relations  will 
permit  of  the  formation  of  at  least  a  general  idea  of  the  probable 
limits  of  the  monthly  run-off,  under  other  rainfall  conditions.  The 
wide  range  of  the  possible  error  of  such  estimates  will  be  shown 
by  the  divergence  of  independent  observations  from  the  normal. 
To  establish  accurately  the  maximum  and  minimum  limits,  it  is 
probable  that  observations,  at  least  as  extended  as  those  needed 
for  accurate  rainfall  estimates,  will  be  needed. 

The  observed  relations  between  the  monthly  rainfall  and  the 
monthly  run-off  in  various  drainage  areas  are  shown  by  Figs.  82,  83, 
84  and  85. 

On  Fig.  82  are  shown  the  relations  of  monthly  rainfall  and  run-off 
for  several  Northern  river  basins,  and  on  Fig.  83  are  shown  the 
same  relations  for  several  Southern  river  basins.  An  examination 
of  these  diagrams  will  show  the  marked  effect  of  seasonal  tempera- 
tures and  conditions  upon  the  quantity  of  run-off.  The  high  per- 
centage of  run-off  in  the  spring  should  be  noted ;  also  how  the  per- 
centages of  run-off  in  these  rivers  drop  with  the  advance  of  the 
season  and  rise  again  in  the  fall. 

On  Fig.  84  are  given  the  monthly  relations  of  rainfall  and  run-off 
for  thirty  years  on  three  small  river  basins  in  the  immediate 
vicinity  of  Philadelphia.  These  drainage  areas,  being  small,  are 
more  readily  and  directly  affected  by  rainfall,  hence  the  relations 
are  much  more  marked  and  uniform  than  those  that  exist  on  larger 
rivers.  The  marked  variation  from  normal  due  to  the  influence  of 
other  varying  conditions  on  the  drainage  area,  especially  during  the 
summer  months,  should  be  noted. 

Figure  85  shows  a  set  of  monthly  diagrams  prepared  by  Emil 
Kuichling,  C.  E.,  for  his  discussion  of  the  relation  of  rainfall  to 
run-off  in  certain  rivers  in  the  Eastern  part  of  the  United  States. 

On  these  diagrams  the  figures  not  enclosed  are  numbers  of  ob- 
servations from  drainage  basins  Nos.  I  to  8  inclusive,  of  the  fol- 
lowing list.  The  figures  enclosed  in  circles  are  the  numbers  of 
observations  from  drainage  basins  Nos.  I  to  28,  inclusive. 


Relations  of  Monthly  Rainfall  and  Run-Off. 


163. 


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Horizontal  Ordinates — Rainfall  in  Inches. 


0  Wisconsin  River  at  Necedah. 
D  Chippewa  River  at  Eau  Claire. 
A  Grand  River  at  Grand  Rapids. 


V  Grand  River  at  Lansing. 
X  Thunder  Bay  River. 
•  Rock  River  at  Rocktoiu 


Fig.  82.  —  Monthly  Rainfall  and  Run-  Off  —  Northern  Rivers. 


164 


Run-Off. 


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Horizontal  Ordinates  —  Rainfall  in  Inches. 

0    Talladega  Creek,  Watershed  Area  156  Square  Miles. 

V  Upadachee  River,          "  "440      " 

•    Alcovy  River  "  "    228      "          " 


Fig.  83. — Monthly  Rainfall  and  Run-Off—Southern  Rivers. 


Relations  of  Monthly  Rainfall  and  Run-Off. 


165 


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I    2   3   4  5   B   7   B   3  ID  II  121314 
RAINFALL    IN    INCHES 


0    I    2    3    4   5    B    7    B    3  ID  II  121314 

RAINFALL    IN    INCHES 
WATERSHED    AREA 
102.2  SQUARE    MILES 


O  B  S  E  RVAT  IONS 
XTOHICKON    CREEK 
ANESHAMINY         "  139.3 

OPERKIOMEN         "  152. 0 

Ffg.  84.— Relation  between  Kainfall  and  Run-Off  on  Tohickon,  Neshaminy,  and 
Perkiomen  Creeks  near  Philadelphia,  Pennsylvania. 


1  66 


Run-Off. 


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Relation  of  Monthly  Rainfall  and  Run-Off.  167 

Watersheds  from  which  Observations  were  platted  on  Diagram  85. 


No. 

Name  of  Basin. 

Area  in  Sq. 
Miles. 

No.  of 
Years 
Record. 

1 

Crotoii  River,  N.  Y   

338  0 

Qrt 

2 

Perkiomen  Creek   Pa 

152  0 

i  q 

g 

Neshaminy  Creek  Pa                                      .  • 

139  3 

1  '\ 

4 

Tohickon  Creek   Pa                                          ... 

10''  2 

14 

5 

Sudbury  River  Mass                         

75  2 

25 

5 

Hemlock  Lake  NY          .  .             

43  i 

12 

Mystic  Lake  Mass                         .    .       

27  7 

18 

8 

Cochituate  Lake  Mass  

19  0 

QQ 

9 

Cayadutta  Creek  N   Y  ,  

40  0 

2 

10 

Saquoit  Creek  N.  Y  

51  5 

2 

11 

Oneida  Creek,  N  Y  

59  0 

2 

12 

Nine-Mile  Creek,  N.  Y  

63  0 

1 

13 

80  8 

1 

14 

E.  Branch  Fish  Creek,  N.  Y  

104  0 

1 

la 

Oriskany  Creek,  N.  Y  

144.0 

2 

](> 

Mohawk  River  N  Y     at  Ridge  Mills 

153  0 

2 

17 

W  Branch  Fish  Creek   N  Y 

187  0 

3 

18 

Salmon  River  N  Y 

191  0 

1 

19 

East  Canada  Creek  N.  Y 

256  n 

2 

20 

West  Canada  Creek  N  Y  . 

518  0 

2 

21 

Schroon  River  N  Y.  . 

563  0 

4 

22 

Passaic  River,  N  J  

822  0 

17 

23 

Raritan  River,  N.  J  

879  0 

3 

24 

Genesee  River,  N.  Y  

1070  0 

25 

Mohawk  River,  N.  Y.,  at  Little  Falls  .  . 

1306  0 

2 

26 

Black  River,  N.  Y  

1889  0 

4 

27 
28 

Hudson  River  N.  Y.,  at  Mechanic  vi  lie,  N.  Y  .  .  .  . 
Muskingum  River,  Ohio  

4500.0 
5828  0 

12 
8 

A  continuous  graphical  record  for  ten  years,  showing  the  rela- 
tions of  rainfall  to  run-off  on  the  Illinois  River  basin,  based  on  ob- 
servations of  stream  flow  made  at  Peoria,  111.,  is  shown  by  Fig.  71. 

93.  Maximum  Stream  Flow. — In  the  construction  of  spillways, 
dams,  and  reservoirs,  and  the  study  of  their  effect  on  the  overflow 
-of  embankments,  levees,  and  lands,  the  question  of  maximum  run- 
off becomes  important. 

Many  formulas  have  been  suggested  by  engineers  for  determin- 
ing flood  flows,  each  of  which  is  based  on  more  or  less  extended 
observations,  and  are  applicable  only  when  used  under  conditions 
similar  to  those  on  which  they  are  founded.  Very  few  of  these 
formulas  take  into  account  the  great  number  of  conditions  that 
modify  the  results.  For  this  reason  most  of  such  formulas  are  of 
little  use  except  for  the  purpose  of  rough  approximation.  None  of 
these  should  be  used  without  a  knowledge  of  the  conditions  under 


i68 


Run-Off. 


Max.  rate  of  Discharge  in  Cu.  Ft.  per  Sec.  per  Sq.  Mile,  (q) 


Maximum  Stream  Flow.  169 

which  they  are  applicable.  Such  calculations  should,  wherever  pos- 
sible, be  based  on  the  known  ratio  of  actual  maximum  and  mini- 
mum flows  on  the  drainage  areas,  or  on  drainage  areas  adjacent  and 
similar  thereto,  and  the  use  of  a  factor  of  safety  as  great  as  the 
importance  of  the  local  condition  will  warrant.  Such  data  serves 
as  the  best  and  most  conservative  guide  for  all  calculations  of  this 
class. 

A  record  of  the  maximum  and  minimum  flows  of  various  Ameri- 
can and  foreign  streams  from  the  report  of  Mr.  Kuichling,  to  which 
reference  has  already  been  made,  is  contained  in  the  Appendix. 

Figure  86  shows  a  graphical  representation  of  the  actual  rate  of 
maximum  flood  discharge  of  these  rivers  and  on  this  diagram  is 
given  the  formulas,  both  graphically  and  analytically,  for  ordinary 
%nd  occasional  maximum  floods  as  proposed  by  Mr.  Kuichling.  It 
is  evident  that  Mr.  Kuichling  has  endeavored  to  represent  the 
maximum  flood  conditions  that  may  occur  on  any  river.  In  many 
localities,  the  results  given  are  much  larger  than  the  actual  condi- 
tions of  flow  will  warrant. 

In  some  cases  the  overflow  of  lands  and  property  by  floods, 
caused  by  back  water  or  otherwise,  may  be  prevented  by  the  con- 
struction of  levees  and  the  installation  of  .pumping  plants  for  drain- 
age purposes.  Under  such  conditions  both  the  extreme  height  pf 
the  flood  and  the  length  of  its  occurrence  become  important  and 
can  be  determined  only  by  gauge  observation.  A  graphical  study 
of  such  data  affords  the  best  means  for  its  consideration.  Figure  87 
shows  hydrographs  of  the  high  water  conditions  on  the  Fraser 
River  at  Mission  Bridge,  British  Columbia.  This  stream  is  fed  by 
the  melting  snows  of  the  foot-hills,  and  the  floods  occur  at  essen- 
tially the  same  time  each  year  within  certain  limits,  as  a  rule  reach- 
ing a  maximum  during  May,  June  or  July.  The  differences  that 
occur  from  year  to  year  are  shown  by  the  different  hydrographs 
which  represent,  however,  gauge  heights  in  feet  and  not  discharges. 
The  highest  record  is  that  of  the  flood  of  June  5,  1894,  of  which, 
however,  no  hydrograph  was  obtained. 

94.  Estimate  of  Stream  Flow. — For  the  purpose  of  estimating 
water  power  no  safe  deduction  can  be  made  from  average  run-off 
conditions,  although  a  knowledge  of  such  conditions  is  desirable. 
The  information  that  is  needed  for  the  consideration  of  water  power 
ic  a  clear  knowledge  of  the  maximum  and  minimum  conditions, 
the  variations  which  occur  between  these  limits  and  a  knowledge 
of  the  length  of  time  during  which  each  stage  is  likely  to  occur 
10 


i7o 


Run  Off. 


-{- 


&i 


i* 


O  »0  00 

Gauge  Height  in  Feet. 


Estimate  of  Stream  Flow.  ±71 

throughout  the  year  or  throughout  a  period  of  years.  As  pointed 
out  in  the  previous  section,  the  extreme  conditions  are  important  in 
considering  the  height  of  flood  as  influenced  by  spillways  and 
other  obstructions  in  the  river.  The  extrejn^jmd^average  low  water 
conditions  commonly  control  or  limit  theexTelirr^i^tlie~pTant  which 
should  be  installed. 

[y~~tne  illustrations  already  shown  it  is  fully  demonstrated 
that  the  run-off  of  any  stream,  either  for  the  year,  period  or  month, 
cannot  be  approximately  expressed  either  as  an  average  amount  or 
as  a  fixed  percentage  of  the  rainfall.  An  expression  showing  the 
relation  between  rainfall  and  run-off  necessarily  assumes  quite  a 
complex  form,  from  which  large  variations  must  be  expected. 
Where  average  amounts  of  run-off  are  considered,  care  must  be 
used  to  base  the  deduction  on  correct  principles.  In  considering  the 
variation  in  the  monthly  flow  of  a  stream,  the  flows  of  such  stream 
should  be  considered  in  the  order  of  their  monthly  discharge 
rather  than,  in  their  chronological  order.  For  example :  in  Table 
XV,  the  mean  monthly  flows,  of  various  streams,  in  cubic  feet  per 
second  per  square  mile  of  drainage  area  are  given.  These  flows 
are  arranged  in  the  chronological  order  of  the  months.  The  aver- 
age monthly  discharges  of  the  streams'  are  calculated  therefrom, 
and  are  shown  in  the  last  column.  An  examination  of  this  table  will 
show  that  the  minimum  monthly  flow  of  a  stream  does  not  always 
occur  during  the  same  month  for  each  year.  For  the  consideration 
of  these  streams  for  water  power  purposes,  the  better  arrangement 
of  the  recorded  flow  is  not  in  the  sequence  of  the  months,  but  by  the 
monthly  periods  arranged  in  the  relative  order  of  the  quantities  of 
flow. 

In  Table  XVI  this  data  has  been  rearranged.  In  this  arrange- 
ment the  least  flow  for  any  month  in  a  given  year  is  placed  in  the 
first  line  and  the  flows  for  other  months  are  arranged  progres- 
sively from  minimum  to  maximum.  The  average  for  each  month 
will,  by  this  arrangement,  give  a  much  better  criterion  of  the 
average  water  power  to  be  expected  from  each  drainage  area  dur- 
ing each  year  than  the  average  monthly  flow  as  determined  in 
Table  XV. 


172 


Run-Off. 


TABLE  XV. 

Mean  Monthly  Flows  of  Various  Eastern  Streams  Arranged  in  Chronological 
Order.     (In  Cubic  Feel  per  Second  per  Square  Mile. ) 

Kennebec  Kiver  at  Waterville,  Me. 
Drainage  Area  4380  sq   miles. 


Year. 

'9:) 

'94 

'95 

'96 

'97 

'98 

'99 

'00 

'01 

'02 

'03 

'04 

'05 

Ave. 

January  .  . 

.60 
.53 
.95 
2.64 
6.92 
3  47 

.37 

.40 
.91 
3.33 
2.17 

.46 
.41 
.45 
5.43 
2.17 
1.46 
.80 
.61 
.40 
.28 
1.27 
1.37 
1.27 

.98 
.64 
2.98 
6.21 
3.87 
1.25 
1.21 
.71 
.77 
.83 
2.07 
.62 
1.84 

.81 
.84 
.86 
5.75 
6.10 
2.94 
2.96 
1.65 
1.04 
.60 
1.29 
1.21 
2.17 

.',3 

2!56 
6.76 
5.70 
2.26 
.89 
.71 
.59 
.92 
1.77 
.59 
1.97 

.53 
.54 
.73 
5.31 
1.81 
2.00 
1.14 
.73 
.43 
.28 
.40 
.51 
1.46 

.54 

2.05 
2.07 
6.45 
6.41 
2.28 
1.31 
.95 
.63 

.<;9 

1.44 
.93 

2.14 

.73 
.57 
1.10 
9.39 
3.46 
1.8S 
1.17 
.95 
.64 
.67 
.55 
1  72 
1.9U 

.88 
.87 
6.57 
5.07 
3.85 
i.4H 
1.79 
1.15 
.96 
1.20 
1.03 
.99 
2.32 

.9i 
.88 
4.42 
3.74 
1.66 
1.52 
1.19 
.88 
.57 
.44 
.33 
.32 
1.41 

2.22 
.20 
.86 
3.41 
4.71 
1.89 
1.22 
1.07 
.98 
1.07 
.77 
.60 
1.58 

.70 

.60 
1.20 
3.08 
2.40 
1.53 
1.07 
.73 
.68 
.40 
.52 
.47 
1.12 

.FC 
.72 
1.97 
5.13 
4.17 
2.14 
1.34 
.87 
,68 

>J9 

.78 

February 

March  

April  .  .  , 

May 

July  

1.81 
.51 
.46 
.53 
.51 
.36 
1.65 

1.30 
.67 
.62 
.85 
.85 
.44 
1.12 

August                                           .... 

September 

October  

November         ....           .   . 

Average  .  .  .  ..  

Merrimac  River  at  Lawrence,  Mass. 
Drainage  Area  4553  sq.  mi. 


Tsar. 

'90 

'91 

'92 

'93 

'94 

'95 

'96 

'97 

'98? 

'99 

'00 

'01 

'02 

'03 

'04 

'o:> 

Ave. 

January  

1.53 
1  70 

2.92 
2.96 
5.19 
4.73 
1.61 
1.00 
.64 
.54 
.56 
.47 
.54 
90 
1.84 

1.87 
.94 
1.61 
1.79 
2.25 
1.28 
1.05 
1.06 
.87 
.47 
1.43 
.86 
1.29 

.65 
1.10 
2.36 
3.42 
4.28 
.97 
.52 
.57 
.61 
.79 
.74 
1.17 
1.43 

.66 
.94 
3.16 
2.43 
1.54 
1.33 
.50 
.37 
.40 
.50 
.78 
.67 
1.11 

.63 
.51 
1.28 
4.35 
1.37 
.67 
.57 
.48 
.37 
.88 
2.10 
2.06 
1.27 

1.44 
2.00 
4.62 
4.00 
.98 
.77 
.45 
.44 
.67 
1  14 
1.46 
.96 
1.58 

.75 
1.01 
2.32 

3.87 
2.22 
2.79 
2.37 
1.12 
.61 
.48 
1.2$ 
2.2K 
1.76 

1.62 
1.71 
4.09 
3.34 
2.42 
1.42 
.58 
.83 
.64 
1.41 
2.17 
1.93 
1.85 

1.73 
1.07 
2.  6-> 
5.81 
2.09 
.65 
.54 
.46 
.44 
.39 
.61 
.61 
1  42 

.74 
3.62 
3.56 
4.06 
2.21 
.87 
.40 
.41 
.33 
.55 
1.28 
1.4.) 
1.63 

72 

.53 
2.04 
3.94 
4.04 
1.61 
.62 
.£6 
.57 
.86 
.65 
2.09 
1.53 

2.24 

1.20 
6.06 
3.72 
2.18 
1.13 
".93 
.81 
.74 
1.54 
1.23 
1.74 
1.96 

.86 
1.99 
5.66 
3.34 
0.94 
2.21 
1.00 
.72 
.51 
.79 
.64 
.80 
1.62 

,57 
.63 
2.64 
4.45 
3.74 
1.00 
.60 
.55 
.6^ 
.78 
.58 
.39 

138 

.83 
.49 
2.2(i 
3.47 
1.12 
.89 
.57 
.58 
1.64 
.70 
.73 
1.82 

,.« 

1.24 
1.40 
3  30 
3.7S 
2  26 
1.27 
.75 
.67 
1  38 
.90 
1.14 
1.29 

March 

3.44 
3.79 
3.14 
1.73 

.69 
.75 
1.84 
2.70 
1.95 
1.44 
2.06 

April 

May  .. 

June 

July  

August  

September  
October  

November  

December 

Average 

Hudson  River  at  Mechanicville,  N.  Y. 
Drainage  Area  4500  sq.  mi. 


Year. 

'88 

'89 

'90 

'91 

'92 

'93 

'94 

,'95 

'96 

'97 

'98 

'99 

'00 

'01 

'02 

'03 

'04 

'05 

Ave. 

January  .... 
February... 
March  
April  
May  
June  .  . 

1.41 

.82 
1.52 
4.73 
4.76 
1.09 
.34 
.38 
.63 
1.02 
2  36 
2.22 
1.77 

2.44 
.84 
1.84 
3.04 
1.97 
1.52 
1.28 
.95 
.41 
.83 
1.77 
2.93 
1.65 

2.50 
1.74 
2.47 
3.35 
3.98 
1.64 
.43 
.45 
1  97 
2.05 
2.03 
.72 
1.94 

1.84 
2.59 
3.94 
4.45 
1.23 
.71 
.52 
.59 
.45 
.33 
.91 
1.91 
1.62 

4.19 
2.06 
2.41 
4.79 
4.37 
2.80 
2.06 
1.22 
.99 
.63 
1.69 
.93 
2.34 

.71 
1.02 
1.97 
3.98 
4.95 
1.07 
.56 
1.11 
1.53 
.86 
.81 
1.60 
1.68 

1.50 
1.07 
3.28 
2.47 
1.68 
1.58 
.70 
.55 
.42 
.81 
1.42 
.97 
1.37 

.86 
.79 
.93 
5.29 
1.52 
.63 
.57 
.87 
.58 
.58 
1.87 
2.42 
1.41 

1.51 
1.04 
3.02 
5.55 
1.02 
1.05 
.62 
.54 
.64 
.91 
2.52 
1.54 
1.66 

.89 
.87 
2.71 
4.24 
2.70 
2.63 
2.47 
1.83 
.61 
.56 
2.22 
3.20 
2.08 

1.72 
1.50 
4.49 
3.05 
2.46 
1.17 
.57 
1.14 
.86 
1.75 
2.05 
1.25 
1.83 

1.49 
1.17 
2.14 

5.25 
2.17 
.58 
.54 
.31 
.46 
.58 
1  49 

1.30 
2.77 
1.72 
5  02 
2.00 
.91 
.52 
.60 
.42 
.47 
1  11 

.69 
.54 
1  80 
6.28 
2.60 
1.73 
.79 
1.03 
.89 
.94 
83 

l"53 
5.53 

2.38 
1.76 
1.40 
1.98 
1.40 
.81 
1.53 
1  41 

1.56 
2.19 
6.87 
3.11 
.78 
1.8S 
l.OF 
1.31 
.91 
2.25 
1  ^ 

1.2J* 
1.52 
2.46 
4.61 
2.96 
1.50 
.58 
1.39 
1.4H 
2.62 
1.03 
.87 
1.86 

1.35 
.79 
2.09 
5.06 
1.82 
2.12 
1.54 
1.25 
2.67 
1.35 

1.60 
1.38 
2.84 
4.15 
2.48 
1.45 
.96 
.94 
.93 
1.12 
1.57 
1.6.' 

July  
August  
September  . 
October  — 
November.  . 
December.  . 
Average  

1.02 
1  43 

1.13 
1  50 

1.88 
1.67 

1.83 
.... 

1.18 
2.03 

Estimate  of  Stream  Flow. 


173 


TABLE  XV.— Continued. 

Potomac  River  at  Point  of  Rocks,  Md. 
9654  sq.  mi. 


Year. 

'98 

'99 

'00 

'01 

'0^ 

'03 

'01 

'05 

Ave. 

January  

2.40 

1.95 

.&3 

.  57 

1.81 

1.78 

.76 

.89 

1.38 

February  

85 

3  00 

1.38 

.37 

3.37 

2  .10 

1.81 

'      .58 

1.71 

March 

1  59 

3  72 

1.93 

1  45 

5.64 

2.77 

1  16 

2  43 

2  58 

Vpril 

1  b7 

1  22 

96 

4  07 

2  99 

2  99 

77 

68 

1  92 

.May  

1  89 

1  20 

45 

2  85 

.02 

.64 

97 

.46 

1  13 

June         

42 

54 

.86 

2  01 

.33 

1  86 

1  05 

.68 

97 

July 

26 

27 

31 

1  11 

32 

1  32 

47 

1  06 

64 

•Vugust     

2  34 

25 

20 

.87 

.26 

.50 

.25 

.60 

.66 

September 

•<!6 

25 

14 

77 

15 

48 

.17 

,3i 

32 

October   

1  45 

.18 

.14 

.40 

.29 

.33 

.12 

.30 

.40 

November 

87 

33 

48 

48 

29 

M 

.14 

24 

38 

December  

1.60 

42 

.64 

2.6-3 

1.96 

.30 

.23 

1.10 

1.11 

Average  

1  30 

1  11 

69 

"   1  46 

1  50 

1  29 

.66 

.78 

From  Table  XVI  it  will  be  seen  that  the  average  minimum 
monthly  flow  of  the  Hudson  River  at  Mechanicville,  N.  Y.,  is  .52 
cubic  foot  per  second  per  square  mile,  the  smallest  monthly  mini- 
mum for  any  year  during  the  period  of  the  observations  being  .31 
and  the  largest  monthly  minimum  for  any  year  being  .81.  On  the 
Potomac  River,  with  a  somewhat  greater,  total  annual  rainfall,  the 
average  minimum  monthly  flow  is  .21,  the  smallest  monthly  mini- 
mum for  the  year  being  .12,  and  the  largest  monthly  minimum  for 
any  year  being  .37.  These  figures,  it  must  be  remembered,  are  aver- 
ages for  each  month,  and  the  actual  minimum  flow  during  the  period 
is  a  much  less  quantity.  These  records  show  that  the  minimum  flow 
GI  a  stream  cannot  be  based  on  the  mean  annual  rainfall.  This  same 


TABLE  XVI. 

Mean  Monthly  Flow  of  Various  Eastern  Streams  Arranged  in  Order  of  their 
.  Magnitude.    (In  Cubic  Feet  per  Second  per  Square  Mile.) 

Kennebec  River  at  Waterville,  Me. 
441  Osq.  mi.  4380  sq  mi. 


Year. 

'93 

'94 

'95 

'96 

'97 

'98 

'99 

'00 

'01 

'02 

'03 

'04 

'05 

Ave. 

Minimum.  

36 

.37 

28 

.62 

.60 

.28 

.59 

.54 

.55 

.87 

.32 

.20 

.40 

46 

.46 

.40 

.40 

.64 

.81 

.43 

59 

.63 

.57 

.88 

.33 

.60 

.47 

.56 

.51 

.42 

.41 

.71 

.84 

.46 

.71 

.69 

.64 

.96 

.44 

.77 

.52 

.62 

.51 

.62 

.45 

.77 

.85 

.51 

.73 

.93 

.67 

.99 

.57 

.86 

.60 

.70 

.53 

.67 

.46 

.as 

1.04 

.53 

.77 

.95 

.73 

1.03 

.88 

.98 

.68 

.78 

.53 

.85 

.61 

.98 

1.21 

.54 

.89 

1  31 

.95 

1.15 

.88 

1.07 

.70 

.90 

.60 

.85 

.80 

1.21 

1.29 

.73 

.92 

1.44 

1.10 

1.20 

.92 

1.07 

.73 

.99 

.95 

.91 

t.27 

1.25 

1.65 

.73 

1.1? 

2.05 

1.17 

1.79 

1.19 

1.22 

1.07 

1.26 

1.31 

1.30 

1.37 

2.07 

2.94 

1.14 

2.26 

3.07 

1.72 

3.48 

1.52 

1.89 

1.20 

1.87 

1.64 

1.77 

1.46 

2.98 

2.96 

2.00 

2.50 

2.28 

1.88 

3.85 

1.66 

2.22 

1.53 

2.23 

3.47 

2.17 

2.17 

3.87 

5.75 

4.81 

5.70 

6.41 

3.46 

5.07 

3.74 

3.41 

2.40 

4.05 

6.9:2 

3.33 

5.43 

6.21 

6.10 

5.31 

6.76 

6.45 

9.39 

6.57 

4.42 

4.71 

3.08 

5.73 

Run-Off. 


TABLE  XVI.— Continued. 

Hudson  River  at  Mechanicville,  N.  Y. 
Drainage  Area  4500  sq.  mi. 


Year. 

'88 

'89 

'90 

'91 

'92 

'93 

'94 

'95 

'96 

'97 

'93 

'99 

'00 

'OL 

'02 

'03 

'04 

'05 

Ave. 

Minimum  .. 

.34 

.44 

.43 

.33 

.63 

.56 

.42 

.57 

.54 

.56 

.57 

.31 

.42 

.54 

.81 

.78 

.58 

.52 

H8 

88 

.45 

45 

93 

71 

55 

58 

(W 

61 

86 

46 

47 

6<1 

91 

87 

79 

66 

.68 

.84 

.72 

.52 

.99 

,81 

.70 

.58 

.64 

.87 

1.14 

.54 

.52 

.79 

1.40 

1.08 

1.08 

.81 

82 

95 

1  64 

.59 

1  22 

86 

,81 

.79 

.91 

,89 

1.17 

.58 

.60 

.83 

1.4(1 

1.18 

1  29 

1  25 

99 

1.02 

1.88 

1.74 

.71 

1.69 

.02 

.97 

.86 

1.02 

1.83 

1.25 

.58 

.91 

.89 

1.41 

1.28 

1.39 

1.35 

1.18 

1  09 

1,52 

1.97 

.91 

2.0fi 

.07 

1.07 

.87 

1.04 

2  22 

1.50 

1.02 

1.11 

.94 

1  .59 

1.31 

1.48 

1,35 

1.34 

1.41 

1.77 

2.03 

1.23 

2.06 

.11 

1.42 

.93 

1.05 

2.47 

1.72 

1.17 

1.13 

1.03 

1.53 

1.56 

1.50 

1.54 

1.48 

1  52 

1.84 

2.05 

1.84 

2.41 

.53 

1.50 

1.52 

1.51 

2.63 

1.75 

1.42 

1.30 

1.73 

1  76 

1.88 

1,52 

1.82 

1.75 

2  22 

1.97 

2.47 

1  91 

2.80 

.60 

1.58 

1.54 

1.54 

2.70 

2.05 

1.49 

1.72 

1,80 

1.8:- 

2,19 

2.46 

2  09 

2.00 

2  3t> 

2  44 

2  50 

2  59 

4.19 

1  97 

1.68 

1,87 

2.52 

2.71 

246 

2  14 

200 

1  88 

1  t.8 

2.:>5 

2  6;' 

2  12 

2.35 

4.73 

2.93 

3.35 

3.94 

4.87 

3.98 

2.47 

2.42 

3.02 

3.20 

3.05 

2.17 

2.77 

•J.60 

>.3f- 

3.11 

2.96 

2.67 

3.12 

Maximum.. 

4.76 

3.04 

3.98 

4.45 

4.79 

4.95 

3.28 

5.29 

5.55 

4.24 

4.49 

5.25 

5.02 

6.28 

5.5t 

6.87 

4.61 

5.06 

4.85 

Merrimac  River  at  Lawrence,  Mass. 
4553  sq.  mi. 


Year. 

'90 

'91 

'92 

'93| 

'94 

'95 

'96 

'97 

'98 

'99 

'00 

'01 

'02 

'03 

'04 

'05 

Ave. 

"Mini  mil  in 

.69 

47 

47 

.52 

37 

37 

.44 

.48 

.58 

.39 

.33 

.53 

74 

.51 

.39 

.49 

48 

.75 

.54 

.86 

.57 

.40 

.48 

.45 

.61 

.64 

.44 

.40 

.57 

'.81 

.64 

.55 

.57 

.59 

.44 

.54 

.87 

.61 

.44 

.57 

.67 

.75 

.83 

.46 

.41 

.62 

.93 

.72 

.57 

.58 

.60 

.53 

.59 

.94 

.65 

.50 

.57 

.77 

1.01 

1.41 

.54 

.55 

.65 

1.13 

.79 

.58 

.70 

.88 

.70 

.64 

1.05 

.74 

.50 

.63 

^96 

1.12 

1.42 

.61 

.74 

.72 

1.20 

.fO 

.60 

73 

.87 

.73 

.90 

1.06 

.79 

.66 

.67 

.98 

1.S8 

1.62 

.61 

.87 

.86 

1.23 

.86 

.62 

.83 

.96 

.84 

1.00 

1.28 

.97 

.67 

.88 

1.14 

2  22 

1.71 

.65 

1.28 

.96 

1.54 

.94 

.63 

.89 

1.12 

.95 

1.61 

1.43 

1.10 

.78 

1.28 

1.44 

2.28 

1.93 

1.07 

1.49 

1.61 

1.74 

1.00 

.78 

1.12 

1.42 

.7.) 

2.92 

1  61 

1.17 

.94 

1.37 

1.46 

2  32 

2.17 

1.73 

2.21 

2.04 

2.18 

1.99 

1.00 

1.22 

1.88 

.14 

2.96 

1.79 

2.36 

1.33 

2.06 

2.00 

2.37 

2.42 

2.09 

3.56 

2.09 

2.24 

2.21 

2.64 

1.64 

2.30 

.44 

4.73 

1.87 

3.42 

2.43 

2.10 

4.00 

2.79 

3.34 

2.62 

3.62 

3.94 

3.72 

3.34 

3.74 

2.26 

3.20 

Maximum  

.79 

5.19 

2.25 

4.28 

3.16 

4.35 

4.62 

3.87 

4.09 

5.81 

4.06 

4.04 

6.06 

5.66 

4.45 

3.47 

4.32 

Potomac  River  at  Point  of  Rocks,  Md. 
9654  sq.    mi. 


Year. 

'98 

'99 

'00 

'01 

'0> 

'03 

"04 

'05 

Ave. 

26 

18 

14 

37 

15 

.22 

.12 

.24 

.21 

.26 

.25 

.14 

.40 

.26 

.30 

.14 

.80 

.26 

.42 

.25 

.20 

.48 

.29 

.33 

.17 

.33 

.31 

.85 

.*7 

.31 

.57 

.29 

.48 

.23 

.46 

.43 

.87 

.33 

.45 

.77 

.32 

.50 

.25 

.58 

.51 

1  45 

.42 

.48 

.87 

.33 

.64 

.47 

.60 

.66 

1.59 

.54 

.64 

1.11 

.62 

1.32 

.76 

.68 

.91 

1.60 

1.20 

.83 

1.49 

1.81 

1.78 

.77 

.68 

1.27 

1.67 

1.22 

.86 

2.01 

1.96 

1.86 

.97 

.89 

1.43 

1.89 

1.95 

.9ti 

2.62 

2.99 

2.30 

1.05 

1.06 

1.85 

2.34 

3.  CO 

1.38 

2.85 

3.37 

2.77 

1.16 

1.10 

225 

Maximum  

2  40 

3  72 

1  93 

4  07 

5  64 

2.79 

1.81 

2.43 

3.01 

fact  is  more  fully  demonstrated  by  the  tables  on  maximum  and  min- 
imum run-off  given  in  the  Appendix.  From  the  data  in  the  Appen- 
dix it  will  be  noted  that  the  recorded  minimum  of  some  of  the 
Southern  streams  is  between  .5  and  .6  cubic  feet  per  second  per 
square  mile,  while  numerous  other  streams  will  vary  from  .2  to  .4; 
nevertheless  a  large  oortion  of  the  streams  shown  have  minimum 
flows  of  .1  and  less. 


CHAPTER  IX. 

RUN-OFF    (Continued). 

95.  Relation  of  Run-Off  to  Topographical  Conditions. — The  rel- 
ative run-off  from  a  drainage  area  depends  largely  on  its  topo- 
graphical condition.  This  is  due  to  the  fact  that  climatic  condition 
depends  on  the  elevation  and  slope  of  the  drainage  area,  and  also 
to  the  fact  that  the  rapid  removal  of  the  water  from  steep  slopes 
assures  less  activity  in  the  other  factors  of  rainfall  disposal  and 
consequently  a  greater  run-off.  Mr.  F.  H.  Newell  in  a  paper  before 
the  Engineering  Club  of  Philadelphia  (see  Proceedings  Engineer- 
ing Club  of  Philadelphia,  vol.  12,  page  144,  1895)  presents  a  dia- 
gram (see  Fig.  88)  which  shows  in  a  broad  way,  the  influence  of 
such  conditions.  In  describing  this  diagram  Mr.  Newell  says : 

"The  diagonal  line  represents  the  limit  or  the  condition  when 
all  of  the  rain  falling  upon  the  surface,  as  upon  a  steep  roof,  runs 
off;  the  horizontal  base,  the  conditions  when  none  of  the  water 


DEPTH  OF  MEAN  'ANNUAL  RUN-OFF  IN  INCHES 
_  M  ro  a 
_  in  a  cn^a  m  c 

7 

z 

/ 

/ 

i 

7 

* 

/ 

// 

^S 

/ 

/ 

/ 

/ 

-^ 

/ 

/ 

/- 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

2 

]        j 

_S 

*S 

0            2 
i    ANNU/ 

5             2 

<L    RAIN 

0           3 
FALL    Ih 

5            4 
1    INCHE 

5        4: 

s 

5            50 

^ 

^ 

5  2 

r  ME  At 


>        i 

D 

A 
D             1. 
EPTH    C 

Fig.  88 


176  Run-Off. 

flows  away.  Between  these  are  the  two  curved  lines,  the  lower  rep- 
resenting the  assumed  condition  prevailing  in  a  catchment  basin  of 
broad  valleys  and  gentle  slopes,  from  which  as  a  consequence  there 
is  relatively  little  flow,  and  the  upper  curve,  an  average  condition 
of  mountain  topography,  from  which  large  quantities  of  water  are 
discharged.  For  example,  with  a  rainfall  of  40  inches  on  an  un- 
dulating catcl  ment  basin,  about  15  inches  is  discharged  by  the 
stream,  while  from  steep  slopes  30  inches  runs  off.  With  less 
mean  annual  rainfall  the  relative  run-off  is  far  less,  as  for  example, 
with  20  inches,  about  7  inches  of  run-off  is  found  in  steep  catchment 
basins,  and  about  3  inches  on  the  rolling  plains  and  broad  valleys 
of  less  rugged  topography.  Following  these  curves  down,  it  would 
appear  that  as  the  average  yearly  rainfall  decreases  the  run-off 
diminishes  rapidly,  so  that  with  from  10  to  15  inches  no  run-off 
may  be  expected  on  many  areas,  and  from  2  to  4  inches  from  the 
mountains.  There  is  an  apparent  exception  to  this,  in  that  with 
very  small  annual  rainfall  the  precipitation  often  occurs  in  what  is 
known  as  cloudbursts,  large  quantities  of  water  falling  at  a  sur- 
prisingly great  rate.  Under  these  conditions  the  proportion  of  run- 
off to  rainfall  increases,  as  the  water  does  not  have  time  to  sat- 
urate the  ground." 

"These  curves  should  not  be  regarded  as  exact  expressions,  but 
as  indicating  general  relationships  and  as  showing  graphically  de- 
ductions based  upon  long  series  of  observations  of  quantities  not 
determined  with  exactness.  Computations  of  this  relation  made 
in  various  parts  of  the  country  have,  when  platted  graphically, 
fallen  near  or  between  these  curves,  according  to  the  character  of 
the  country  from  which  the  water  was  discharged.  On  the  figure 
are  shown  three  average  determinations,  numbered  i,  2  and  3,  rep- 
resenting respectively  the  relation  of  run-off  to  rainfall,  for  the 
Connecticut,  Potomac  and  Savannah  Rivers.  The  horizontal  lines 
indicate  determinations  made  for  western  streams  coming  from 
areas  of  small  precipitation.  The  exact  amount  of  rainfall  is  not 
known,  as  the  observations  are  not  representative  of  the  conditions 
prevailing  upon  the  mountains,  and  therefore  the  horizontal  line  has 
been  used  instead  of  a  dot,  as  indicating  the  probable  range  of 
rainfall,  as,  for  example,  being  from  10  to  15,  or  from  15  to  20 
inches.  The  height  of  these  short  lines  above  the  base  indicates 
the  average  annual  run-off  of  the  basin,  a  quantity  which  has  been 
determined  with  considerable  accuracy  according  to  the  method 
just  described." 


Effects  of  Geological  Conditions  on  the  Run-Off.  177 

Figure  88  is  presented  on  account  of  the  .general  principles 
illustrated  thereby  and  should  be  used  for  such  purpose  only. 
While  the  limits  given  by  Mr.  Newell  are  sufficiently  broad  to 
include  many  of  the  conditions  in  the  United  States,  they  are  too 
broad  to  give  a  sufficiently  definite  relation  for  most  local  conditions 
and  too  narrow  to  include  all  conditions  which  may  occur  in  the 
United  States.  The  latter  fact  is  perhaps  best  illustrated  by  Fig, 
89,  reproduced  from  a  paper  by  Messrs.  J.  B.  Lippincott  and  S.  G. 
Bennett  on  "The  Relation  of  Rainfall  to  Run-Off  in  California", 
published  in  the  Engineering  News,  vol.  47,  page  467.  This  figure 
shows  the  annual  and  mean  run-off  from  various  California  drain- 
age areas  based  on  several  years'  observations.  The  diagram  shows 
both  the  Newell  curves,  illustrated  in  Fig.  88,  and  three  mean  curves 
for  California  conditions,  also  several  mean  and  numerous  annual 
run-off  observations  which  can  be  studied  in  detail  in  the  article 
above  referred  to.  The  general  curve  for  large  drainage  areas  is 
for  areas  of  100  square  miles  or  over. 


S  10  IS  20  25 


ANNUAL    RAINFALL   IN    INCHES 


Fig.  89 

96.  Effects  of  Geological  Condition  on  the  Run-Off. — The  geo- 
logical condition  of  a  drainage  area  has  a  marked  effect  on  the 
run-off.  The  determination  of  the  exact  geological  conditions  of 
any  drainage  area,  which  control  or  modify  the  resulting  run-off, 
is  difficult  or  even  impossible  and  can  seldom  be  done  with  suf- 
ficient accuracy  so  that  the  results  may  be  even  approximated  with- 
out actual  observations  on  the  drainage  areas.  The  effects  of  these 
conditions,  however,  are  important  and  they  are  here  pointed  out 


Run-Off. 


so  that  such  effects  may  be  realized  and  the  fact  appreciated  that 
the  run-off  of  streams  otherwise  similarly  located  may  be  materially 
different  on  account  of  difference  in  these  conditions.  A  good  ex- 
ample of  the  geological  influence  on  run-off  may  be  seen  by  compar- 
ing the  stream  flow  of  any  of  the  Northern  Wisconsin  streams  with 
that  of  the  Rock  River  in  the  Southern  portion  of  the  state.  Most 
of  the  Northern  Wisconsin  streams  flow,  in  part,  over  pervious 
beds  of  sand-stone  and  a  considerable  amount  of  the  water  falling 
on  their  drainage  areas  is  undoubtedly  lost  through  absorption  by 
the  underlying  strata.  These  losses  undoubtedly  affect  the  flow  of 
the  stream  to  a  considerable  extent.  These  streams,  however,  have 
no  large  under-flow  through  loose  material  which  can  absorb  and 
transmit  any  considerable  portion  of  the  rainfall  that  would  other- 
wise appear  as  surface  run-off.  The  Rock  River,  on  the  other  hand, 
follows  for  a  considerable  portion  of  its  course  through  Wisconsin, 
its  pre-glacial  drainage  valley  which  is  filled  to  a  depth  of  300  feet 
or  more  with  drift  material  consisting  largely  of  sands  and  gravels 
through  which  a  large  amount  of  water  doubtlessly  escapes.  The 

TABLE  XVII. 

Comparative  Mean  Monthly  Run-Off  of  ihe  Wisconsin  River  at  Necedah,  Wis- 
consin,  and   the  Rock  River  at  Rock! on,   Illinois,   in   Cubic  Feet 
Per  Second  Per  Square  Mile. 

19O3. 


g 

H-5 

& 

r° 
EH 

jj 

1 

h 

Cu 

<< 

>, 

c3 

g 

s 

3 

1-5 

j>> 

3 

H-5 

M 

% 

a 

CD 

OQ 

+3 

o 

o 

> 

0 

ft 

6 
a> 
P 

Wisconsin  river  

45 

44 

0  04 

1   48 

9  50 

1      IP 

1  56 

1   15 

9  73 

1   83 

86 

1   34 

Rock  river 

91 

6i 

91 

78 

44 

45 

1904. 


Wisconsin  river  
Rock  river 

45 

77 

2  80 

2.21 
1  76 

2.63 

88 

1.96 
39 

1.02 
?6 

.66 
?4 

.90 
38 

2.34 
50 

.98 

30 

41 

1905. 


Wisconsin  river  

1.56 
2.10 

2.72 
1.63 

1.91 
1.10 

4.02 
1.06 

1.50 
.64 

1.05 
.4] 

1.28 
.41 

.99 

.39 

.81 

.40 

1.53 
.44 

Rock  river  

.60 

.53 

19O6. 


^Wisconsin  river  

3  90 

1  81 

1   86 

1   13 

90 

89 

83 

1.17 

1  41 

Rock  river  

1  56 

1   59 

1   9? 

1.49 

58 

37 

38 

10 

?1 

?8 

Effects  of  Area  on  the  Run-Off.  179 

deposits  of  this  old  river  bed  have  been  quite  extensively  explored 
for  water  supply  purposes  and  yield  very  large  quantities  of  water 
for  domestic  and  manufacturing  supplies.  Most  of  the  under-flow, 
however,  undoubtedly  passes  away  to  an  unknown  outlet  as  the 
modern  river  leaves  the  old  valley  near  Rockford,  111. 

A  comparison  between  mean  monthly  flows  of  the  Wisconsin  and 
Rock  Rivers,  as  shown  in  Table  XVII,  will  give  an  idea  of  the  effect 
of  these  different  conditions  as  shown  by  the  run-off  of  these  two- 
rivers. 

97.  The  Influence  of  Storage  on  the  Distribution  of  Run-Off. — 
Favorable  pondage  conditions  on  a  watershed  have  an  important* 
effect  on  the  distribution  of  the  run-off,  and  this  effect  is  readily 
discernible  in  the  records  of  flow  from  such  areas. 

Figure  90  is  a  hydrograph  of  the  discharge  of  the  various  rivers 
draining  the  Great  Lakes  for  the  years  .1882  to  1902.  A  general 
similarity  is  seen  in  the  annual  variations  in  these  hydrographs  and 
yet  there  is  a  considerable  variation  from  the  maximum  to  the 
minimum  discharge  in  accordance  with  the  rainfall  and  other  condi- 
tions prevalent  on  the  watershed.  In  every  case,  however,  the 
minimum  of  the  year  is  found  to  occur  at  about  the  same  time,  and 
the  time  of  maximum  height  is  also  fairly  constant.  The  ratios 
between  maximum  and  minimum  flow  are  very  much  less  than  those 
that  obtain  on  other  watersheds  where  the  pondage  area  is  much 
less. 

In  the  St.  Lawrence  River  the  maximum  mean  monthly  discharge 
is  about  320,000  second  feet,  and  the  minimum  is  about  185,000 
second  feet,  the  maximum  being  not  quite  double  the  minimum.  In 
the  discharge  of  the  Niagara  River  the  maximum  mean  monthly 
discharge  is  about  260,000  cubic  feet,  and  the  minimum  about 
175,000,  the  fluctuation  being  still  more  moderate. 

The  mean  monthly  discharge  of  the  St.  Marys  River  shows  a 
maximum  of  about  110,000  second  feet,  and  a  minimum  of  about 
50,000.  The  ratio  here  is  somewhat  higher,  because,  in  this  case, 
Lake  Superior  and  its  drainage  area  being  the  source  of  supply, 
the  relation  of  pondage  to  drainage  area  is  less  than  in  the  com- 
bined lakes,  and  the  effect  is  seen  in  the  variation  in  the  discharge 
of  this  river. 

98.  Effects  of  Area  on  the  Run-Off. — The  size  of  the  drainage 
area  of  any  stream  has  a  marked  effect  on  the  distribution  of  the 
run-off.     The  hydrographs  of  small    areas    show    the    effects    of 
heavy  rains   by  an   immediate   and   marked   increase   in   the   flow. 


i  So 


Run-Off. 


The  Study  of  a  Stream  from  its  Hydrographs.  181 

This  is  well  shown  by  a  comparison  of  the  hydrographs  of  Per- 
kiomen  Creek  and  the  Kennebec  River  (Fig.  96),  and  of  the 
Hood  and  Spokane  Rivers  (Fig.  99).  On  small  streams  where  per- 
vious deposits  are  largely  developed,  the  rainfall  is  rapidly  absorbed 
and  does  not  so  radically  affect  the  run-off.  Large  streams  do  not 
feel  the  immediate  effect  of  rainfall,  on  account  of  the  time  required 
for  the  run-off  to  reach  the  main  stream.  The  flow  of  large  streams 
is  also  modified  by  the  fact  that  uniform  conditions  of  rainfall 
seldom  obtain  on  the  entire  area.  On  large  drainage  areas,  condi- 
tions of  rainfall  may  prevail  on  one  or  more  of  the  tributaries  only, 
while  on  other  portions  of  the  drainage  area  the  conditions  may 
be  quite  different.  Such  conditions  may  frequently  be  reversed, 
with  the  result  that  the  larger  the  stream  the  less  becomes  the 
extremes  of  flow  and  the  greater  the  uniformity  of  flow. 

99.  The  Study  of  a  Stream  From  Its  Hydrographs. — The  influ- 
ences of  various  factors  on  the  run-off,  as  above  discussed,  can  be 
clearly  seen  from  an  analysis  of  the  stream  flow  data,  but  they  can 
best  be  appreciated  by  noting  their  effect  on  the  hydrograph.  The 
hydrograph  of  the  actual  flow  of  a  stream  is  the  best  means  of 
studying  its  manifold  variations,  but  to  fully  comprehend  the  wide 
limit  of  such  variations,  hydrographs  must  be  available  for  a 
long  term  of  years.  When  the  hydrographs  are  sufficiently  ex- 
tended to  cover  all  of  the  usual  variations  in  rainfall  and  other 
meteorological  conditions,  they  afford  a  comprehensive  view  of 
the  entire  subject  of  the  run-off  of  the  stream. 

Figures  91  and  92  show  hydrographs  of  the  Passaic  River  for 
seventeen  years.  From  these  hydrographs  the  actual  variations  in 
flow  as  they  have  occurred  on  this  drainage  area  during  this  period 
can  be  seen.  The  average  monthly  rainfall  on  the  drainage  area  has 
also  been  shown  on  these  diagrams  and  the  effects  of  such  rainfall 
on  the  run-off  should  be  noted.  It  is  important  to  note  especially 
the  marked  effect  of  a  limited  rainfall  during  the  months  of  the 
storage  period,  when  the  ground  has  previously  become  saturated, 
as  compared  with  the  effects  of  the  same  or  greater  rainfalls  during 
the  growing  period,  when  the  ground  water  has  been  partially  ex- 
hausted by  the  demands  of  vegetation  and  the  draft  of  the  low 
water  flow. 

In  these  diagrams,  and  those  following,  the  flows  are  shown 
in  cubic  feet  per  second  per  square  mile,  in  order  that  their 
value  for  comparative  purposes  may  be  increased.  The  absolute 
discharge  of  a  river  in  cubic  feet  per  second  gives  no  comparative 


182 


Run-Off. 


2.40    I  2^2  I    4.12       £-89    I    0.61        U4    |  7.69 


Figures  near  top  of  each  diagram  show  total  monthly  rainfall. 
Fig.  91.— Daily  flow  of  Passaic  River,  Little  Falls,  N.  J. 


The  Study  of  a  Stream  from  its  Hydrographs.  183 


^  8 

2  6 

JT  » 

I 

^  12 

§  10 

I  « 


3  i 

G 
O) 

£?  12 

I    10 

tn      8 

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2 


Figures  near  top  of  each  diagram  show  total  monthly  rainfall. 
Fig   92. — Daily  flow  of  Passaic  River,  Little  Falls,  N.  J. 


184  Run-Off. 

measure  of  discharge  values,  but  when  the  corresponding  area  is 
also  shown,  the  diagram  becomes  more  or  less  applicable  for  com- 
parative purposes  to  other  areas.  Hence,  for  general  or  compara- 
tive discussion,  the  discharge  per  unit  of  area  should  be  the  basis 
of  consideration. 

100.  Comparative  Run-Off  and  Comparative  Hydrographs. — In 
studying  and  comparing  all  run-off  data  and  the  hydrographs  based 
thereon  it  is  important  to  note  that  a  uniformity  of  conditions  pro- 
duces a  uniformity  of  results.  Such  data  is  not  only  of  value  in 
the  study  of  the  river  from  which  it  is  obtained,  but  also  furnishes 
information  regarding  other  streams  that  exist  under  the  same  or 
similar  conditions,  both  physical  and  meteorological. 

Table  XVIII,  which  shows  the  monthly  run-off  for  a  term  of  years 
of  certain  Michigan  streams,  gives  a  comparison  of  the  flow  of 
streams  under  such  conditions,  as  expressed  by  their  comparative 
monthly  run-off.  The  relative  geographical  locations  of  these 
streams  are  shown  in  figure  93.  The  run-off  from  each  drainage 
area  is  given  in  cubic  feet  per  second  per  square  mile,  so  that  the 
results  are  strictly  comparable,  the  question  of  size  of  area  being 
eliminated.  A  general  resemblance  can  be  traced  between  most  of 
these  streams.  The  Manistee  and  Au  Sable  Rivers,  in  the  Northern 
portion  of  the  state,  have  sand  and  othef  pervious  deposits  largely 
developed  on  their  drainage  areas,  and  show,  in  consequence, 
greater  uniformity  of  flow  and  a  greater  mean  flow  than  that  of 
the  other  streams. 

Comparative  hydrographs  of  some  of  these  streams  for  the  year 
1904  are  shown  in  Fig.  94.  The  vertical  scale  for  each  of  the 
hydrographs  shown  on  the  diagram  is  the  same,  and  represents  the 
discharge  in  cubic  feet  per  second  per  square  mile.  The  relative 
flows  of  the  different  streams  are  thus  easily  compared.  On  these 
diagrams  has  also  been  shown  the  average  rainfall  which  occurred 
on  each  drainage  area  for  each  month.  A  study  of  the  rainfall 
record  in  connection  with  the  flow  lines  of  the  hydrograph,  will 
show  that  the  difference  in  flow  is  not  entirely  attributable  to  the 
prevailing  rainfall  conditions  on  the  drainage  area,  but  that  other 
physical  influences  have  a  material  effect.  These  hydrographs 
were  originally  prepared  in  order  to  form  a  basis  for  an  estimate 
of  the  probable  horse  power  on  the  White  River,  on  which  no 
gauge  readings  had  been  taken.  On  the  right  of  the  diagram  is 
shown  a  horse  power  scale  from  which  the  probable  power  of  the 
White  River,  with  a  given  fall  and  drainage  area,  and  on  the  basis 


Comparative  Hydrographs. 


185 


Fig.  93. — Map  showing  location  of  various  Michigan  drainage  areas. 
11 


i86 


Run-Off. 


3*6 


BRAND       RIVER       AT       NORTH 
3.86          2.18          3.64         2.74  1.91 


LANS 
3.60 


20000  a 


a   ' 


GRAND       RIVER       AT     CRAN 
2.48     I     3.62      I      IJ9 


RAPID 
2.89 


80000 
40000 


299 


AJ  SABLE:     RIVER 


3.14          344 


Fig.  94. — Comparative  Hydrographs  of  Various  Michigan  Rivers  for  the  year 

1904. 


Comparative  Hydrographs. 

33VONOd     HUM      SHOOK     H3MDd    16UOK 


I87 


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2 
o 

s 


311ft    3HVnl)S    «3d    ON033S    U3d    133J 


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i88 


Run-Off. 


TABLE  XVIII. 

Discharge  in  cubic  feet  per  second  per  square  mile  of  drainage  area  of  various 

Michigan  rivers. 


Ihunder 
Bay  river 
at  Alpena 

At  Grand  £ 
Rapids.  § 

f-b 

river 

&b 

-u.3 
<1  § 

Kalamazoo 
river  at 
Allegan. 

St.  Joseph 
river  at 
Buchanan. 

Muskegon 
river  at 
Newayga. 

Manistee 
river  at 
Sherman. 

Au  Sable 
river  at 
Bamfield. 

White  river 
at  Moran's 
Bridge. 

1901 
March  

3.25 

2  73 

April  

1.49 

1.39 

1  06 

64 

1  29 

May  

1.18 

.66 

48 

.53 

76 

June  ...   

.63 

49 

34 

57 

53 

45 

July  

.74 

.92 

78 

51 

45 

45 

August  

.51 

.38 

58 

52 

38 

40 

September  

1.31 

.39 

.44 

.50 

54 

37 

October  

.70 

.47 

.51 

50 

71 

50 

November  .  .  .'  

.41 

.42 

.35 

57 

.70 

38 

December  

.32 

.65 

.66 

.54 

.82 

.38 

1902 
January  

40 

.46 

.55 

.46 

69 

30 

29 

.40 

43 

.46 

.62 

.33 

March  

1.31 

1.41 

1  26 

.58 

1  32 

57 

April  

.91 

1.03 

1.02 

.55 

90 

1.03 

Alay 

78 

1.15 

1  09 

55 

98 

1  34 

June  

.74 

.70 

.88 

.56 

.92 

.77 

July 

40 

1.57 

1  78 

.62 

1  10 

.64 

August 

46 

.53 

57 

54 

60 

.47 

71 

September           .   .  . 

.21 

.57 

50 

.52 

.58 

.46 

71 

October        

48 

.79 

84 

.61 

.84 

•  67 

.75 

November  

77 

.95 

.66 

.63 

79 

•  57 

95 

December  

.34 

.96 

.62 

.64 

1.00 

.54 

.91 

Yearly  mean  

.59 

.88 

.85 

.56 

.86 

.68 

1903 
January  

.44 

1.53 

83 

93 

1.13 

1  48 

February  ....  ,  

55 

2.26 

1.36 

1  20 

1.52 

.67 

1.18 

March  

1.67 

2.13 

2.69 

1.84 

2.05 

1.58 

1.43 

April 

1  16 

2.04 

2  45 

1  63 

1  76 

1.38 

1  38 

May 

62 

.68 

52 

.76 

.91 

.97 

June        » 

44 

.53 

46 

.69 

.78 

July. 

48 

.45 

53 

.62 

22 

.79 

August  

.83 

52 

.79 

.69 

40 

1.03 

September  

.79 

1  06 

1,04 

.92 

40 

1.01 

October 

.68 

1  15 

62 

81 

35 

.86 

November 

43 

54 

43 

68 

41 

28 

•  78 

December.   .  . 

.38 

62 

33 

.72 

.66 

41 

1.13 

Yearly  mean  

1904 
January  . 

.71 

.38 

1.05 

1.00 
48 

.93 

.82 

1  49 



1  28 

1.07 
1.94 



February 

46 

1  07 

98 

1  48 

1  18 

2  35 

March 

64 

3  05 

3.44 

3  07 

1  29 

1.79 

April  

3.48 

2.90 

2.22 

2.08 

2.24 

2.35 

1.89 

May 

1  79 

1.00 

69 

1.03 

95 

2  00 

1.49 

June  .  . 

1.17 

.52 

.33 

.73 

.68 

1.42 

1,05 

Comparative  Hydrographs. 


189 


TABLE  XVIII.— Continued. 


•~    S3 

«  y  ? 
I-£| 

2  ^ 

H«3 

At  Grand  J 
Rapids,  g 

0. 

river 
£ 

51 

Kalamazoo 
river  at 
Allegan. 

St.  Joseph 
river  at 
Buchanan. 

Muskegon 
river  at 
Newayga. 

Manistee 
river  at 
Sherman. 

3^2 

-*i 

5>§ 

•"J'CPQ 

O>    02 
•  £"& 

*H     CS         . 

So£ 
£^3 
£^c5 

July 

36 

35 

25 

66 

67 

1  22 

90 

46 

August 

36 

29 

24 

.55 

45 

1  18 

85 

66 

September  
October        

.34 

38 

.35 
.59 

.21 
.32 

.61 

71 

.33 

.47 

.33 
.45 

l.ll 
1  19 

.77 
82 

.68 
93 

November  
December  

.35 
.35 

.37 

.24 
.26 

.55 

.56 

.47 

.40 

.42 
.39 

1.09 
1  08 

.76 
1.37 

.79 
.94 

Yearly  mean  

.84 

.78 

1.06 

1.36 

1.33 

Mean  for  last  5  or 
6  months 

.35 

41 

25 

61 

47 

41 

1  14 

91 

74 

1905 
January  

"fi3 

1  20 

1.31 

1  34 

February  

67 

1  31 

1.97 

1  51 

March 

1  94 

1  52 

1  19 

1  55 

April 

1  47 

1  81 

1  07 

1  55 

Mav 

1  40 

1  51 

1.14 

1  47 

June 

2  76 

1  29 

.98 

1.84 

Mean  for  6  mos.  .  . 

1.49 

1.61 

1.11 

1.54 

of  the  comparative  flows  of  various  Michigan  rivers,  could  be  es- 
timated. In  Fig.  95  these  hydrographs  have  been  re-drawn,  the 
daily  flows  being  platted  in  the  order  of  their  magnitude.  This 
form  of  diagram  represents  the  best  basis  for  the  comparative 
study  of  stream  flow  for  power  purposes  where  storage  is  not 
considered,  and  where  the  continuous  power  of  the  passing  stream 
is  to  be  investigated. 

A  careful  study  of  Figs.  94  and  95  will  show  that  the  run-off  is 
similar  in  streams  situated  under  similar  geographical,  topograph- 
ical, and  geological  conditions,  and  having  equal,  or  similar,  rain- 
falls on  the  drainage  area.  The  departure  of  the  various  streams 
here  considered,  from  the  average  of  all,  gives  a  very  clear  idea  of 
the  errors  which  may  be  expected  in  estimating  the  flow  of  any  par- 
ticular stream  from  the  hydrographs  of  other  adjacent  streams,  or 
from  the  flow  of  streams  more  remote,  and  which  are  located  under 
•different  physical  conditions. 

10 1.  Comparative  Hydrographs  From  Different  Hydrological 
Divisions  of  the  United  States. — The  hydrographs  oif  streams  differ 
widely  in  character,  both  in  accordance  with  their  geographical 
location  and  the  diverse  physical  character  of  their  drainage  areas. 
Their  geographical  location  affects  their  climatic,  geological  and 


ipo 


Run-Off. 


Kennebec  River,  Waterville,  Me.:  Drainage  Area,  4410  Sq.  Mi. 


Perkiomen  Creek,  Frederick,  Pa.:  Drainage  Area,  152  Sq.  Mi. 


Yadkin  River,  Salisbury,  N.  C.:  Drainage  Area,  3399  Sq.  Mi. 


1903 


1904 


Alcovy  River,  Covington,  Ga.:    Drainage  Area,  228   Sq.  Mi. 


Coosa  River,  Riverside,  Ala.:    Drainage  Area,  70G5   Sq.  Mi. 


I 


1903 


Creek,  Nottingham,  Ala.:   Drainage  Area,  156  Sq.  Mi. 
Fig.  96. — Hydrographs  of  Atlantic  and  Eastern  Gulf  Drainage. 


Comparative  Hydrographs. 


191 


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Licking  River,  Pleasant  Valley,  O.,  Drainage  Area  690  Sq.  Mi. 

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Seneca  River,  Baldwinsville,  N.  Y.,  Drainage  Area,  3103  Sq.  Mi. 

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Chittenango  Creek,  Chittenango,  N.  Y.,  Drainage  Area,  79  Sq.  Mi. 

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Iron  River,  near  Iron  River  Mich.,  Drainage  Area  75  Sq.  Mi. 
g  97. — Hydrographs  of  Ohio  Valley  and  St.  Lawrence  Drainage. 


I92 


Run-Off. 


i 


1903 


£S 


1904 


Wisconsin  River,  Necedah,  Wis.,  Drainage  Area,  5800  Sq.  Mi. 


1903 


1904 


Meramec  River,  Eureka,  Mo.,  Drainage  Area,   3497   Sq.   Mi. 


1903 


104 


Otter  Creek,  Mountain  Park,  Okla.,  Drainage  Area,  126  Sq.  Mi. 


Clear  Creek.  Buffalo.  Wyo.,  Drainage  Area,  116  Sq.  Mi. 


Yellowstone  River,  Livingston,  Mont.,  Drainage  Area,  3580  Sq.  Mi. 


Niobrara  River,  Valentine,  Neb.,  Drainage  Area,  6070  Sq.  Mi. 


1803 


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Rio  Grande  River,  Labatos,  N.  M.,  Drainage  Area,  7695  Sq.  Mi. 


1903 

191 

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Salt  River,  McDowell,  Ariz.,  Drainage  Area,  6260  Sq.  Mi. 
Fig.  98.— Hydrographs  of  Mississippi  Valley  and  Gulf  Drainage. 


Comparative   Hydrographs. 


193 


Spokane  River,  Spokane,  Wash.,  Drainage  Area,  4005  Sq.  Mi. 


Hood  River,  Tucker,  Ore.,  Drainage  Area,  350  Sq.  Mi. 


Kalawa  River,  Forks,  Wash.,  Drainage  Area,  213  Sq.  Mi. 


1903 

1904 

^Tr 

y&r. 

Kern  River,  Bakersfield,  Cal.,  Drainage  Area,  2345   Sq.  Mi. 


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1903 

1904 

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San  Gabriel  River,  Azusa,  Cal.,  Drainage  Area,  222  Sq.  Mi. 


Bear  River.  Collinston,  Utah,  Drainage  Area,  6000  Sq.  Mi. 


Walker  River,  Coleville,  Cal.,  Drainage  Area,  306  Sq.  Mi. 
Fig.  99.— Hydrographs  of  Western  Drainage. 


194  Run-Off. 

topographical  conditions,  and  results  in  a  material  difference  in 
the  distribution  and  quantity  of  run-off. 

Hydrographs  from  the  various  hydrological  divisions  of  the 
United  States  are  shown  by  Figs.  96  to  99,  inclusive.  For  each 
drainage  area  hydrographs  for  two  years  are  shown  in  order  to 
eliminate,  partially  at  least,  the  effect  of  any  peculiar  conditions 
which  might  have  obtained  during  a  single  year,  and  to  show  that 
the  hydrographs  are  characteristic. 

102.  General  Conclusions. — A  complete  discussion  of  run-off  is 
impossible  in  the  space  available  in  this  volume.  Attention  has 
been  called  to  the  general  laws  upon  which  the  amount  of  run-off 
depends,  and  to  the  similarity  in  flow  that  obtains  on  watersheds 
which  are  physically  similar,  also  to  the  variations  in  run-off  that 
occur  on  different  watersheds  due  to  differences  in  physical  condi- 
tions. 

Each  stream  presents  peculiarities  of  its  own,  and  in  investigating 
stream  flow  the  data  available  is  seldom  the  same  and  is  always 
found  to  be  much  too  limited  for  a  complete  understanding.  Only 
general  suggestions  can  be  offered  for  the  study  and  investigation 
of  these  subjects.  Attention  has  been  directed,  as  clearly  as  pos- 
sible, to  the  errors  which  are  likely  to  arise  in  the  investigation  of 
water  power  conditions  by  comparative  study.  From  a  knowledge 
of  such  errors  the  engineer  will  realize  the  limiting  values  of  his 
conclusions,  and  hence  'should  so  shape  his  design  as  to  effect  as 
safe  a  construction  as  the  condition  will  permit,  and  also  a  construc- 
tion which  will  bear  out  fairly  well  his  conclusions  at  the  time  of  its 
inception.  It  is  evident  that  no  exact  conclusions  are  possible  in 
these  matters,  and  that  an  element  of  uncertainty  is  always  pres- 
ent. A  knowledge  of  the  extent  of  these  uncertainties  and  the 
probable  limits  of  exact  knowledge  are  as  important  to  the  engineer 
as  his  ability  to  draw  correct  conclusions  from  data  which  is  known 
to  be  correct. 

LITERATURE. 

RESULTS   OF   STREAM   FLOW    MEASUREMENTS. 

1.  Annual  Reports  of  the  Water  Bureau  of  Philadelphia.     Contain   com- 

plete data  relating  to  the  Perkiomen,  Tohickon  and  Neshaminy. 

2.  Monthly  Data  Relating  to  the  Sudbury,  Cochituate,  and  Mystic.    Reports 

of   the   Boston   Water   Board,   and   of   the   Metropolitan   Water 
Board,  Boston. 

Publications  of  the  U.  S.  Geological  Survey  contain  data  for  the  years 
indicated  below : 


Literature. 

3.  1888.  Tenth  Annual  Report.     Part  I. 

4.  1889.  Eleventh  Annual  Report.     Part  II. 

5.  1890.  .  Twelfth  Annual  Report.     Part  II. 

6.  1891.  Thirteenth  Annual  Report.     Part  III. 

7.  1892.  Fourteenth  Annual  Report.    Part  II. 

8.  1893.  Bulletin  No.  131. 

9.  1894.  Sixteenth  Annual  Report.     Part  II. 

10.  1894.  Bulletin  No.  131. 

11.  1895.  Seventeenth  Annual  Report.    Part  II. 

12.  1895.  Bulletin  No.  140. 

13.  1896.  Eighteenth  Annual  Report.     Part  IV. 

14.  1896.  Water  Supply  and  Irrigation  Paper,  No.  11. 

15.  1897.  Nineteenth  Annual  Report.     Part  IV. 

16.  1897.  Water  Supply  and  Irrigation  Papers,  Nos.  15  and  16. 

17.  1898.  Twentieth  Annual  Report.     Part  IV. 

18.  1898.  Water  Supply  and  Irrigation  Papers,  Nos.  27  and  28. 

19.  1899.  Twenty-first  Annual  Report.    Part  IV. 

20.  1899.  Water  Supply  and  Irrigation  Papers,  Nos.  35  to  39,  inclusive. 

21.  1900.  Twenty-second  Annual  Report.     Part  IV. 

22.  1900.  Water  Supply  and  Irrigation  Papers,  Nos.  47  to  52,  inclusive. 

23.  1901.  Water  Supply  and  Irrigation  Papers,  Nos.  65,  66  and  75. 

24.  1902.  Water  Supply  and  Irrigation  Papers,  Nos.  81  to  85,  inclusive. 

25.  1903.  Water  Supply  and  Irrigation  Papers,  Nos>.  97  to  100,  inclusive. 

26.  1904.  Water  Supply  and  Irrigation  Papers,  Nos.  124  to  135,  inclusive. 

27.  1905.  Water  Supply  and  Irrigation  Papers,  Nos.  165  to  178,  inclusive. 

RELATIONS    OF   RAINFALL   AND    STREAM   FLOW. 

28.  Fteley,  A.    The  Flow  of  the  Sudbury  River,  Mass.    Trans.  Am.  Soc.  C.  E. 

Vol.  10,  p.  225,  1881. 

29.  Lawe®,  J.  B.     On  the  Amount  and  Composition  of  Rain  and  Drainage 

Waters,  collected  at  Rothamsted.     Jour.  Royal  Agric.  Soc.  Eng. 
Vol.  17,  p.  241,  1881,  and  Vol.  18,  p.  1,  1882. 

30.  Coghlan,  T.  A.    Discharge  of  Streams  in  Relation  to  Rainfall,  New  South 

Wales.    Proc.  Inst.  C.  E.,  Vol.  75,  p.  176,  1884. 

31.  Croes,  J.  J.  R.     Flow  of  the  West  Branch  of  the  Croton  River.     Trans. 

Am.  Soc.  C.  E.,  Vol.  3,  p.  76.    May,  1884. 

32.  Brackett,  Dexter.     Rainfall  Received  and  Collected  on  the  Water-sheds 

of  Sudbury  River  and  Cochituate  and  Mystic  Lakes.   Jour.  Asso. 
Eng.  Soc.,  Vol.  5,  p.  395,  1886. 

33.  McElroy,   Samuel.     The  Croton  Valley  Storage.     Jour.   Asso.  Eng.   Soc. 

1890. 

34.  Fitzgerald,  Desmond.     Rainfall,  The  Amount  Available  for  Water  Sup- 

ply.    Jour.  New  Eng.  W.  Wks.  Assn.     1891 

35.  Fitzgerald,   Desmond.     Yield   of  the   Sudbury  River   Watershed   in   the 

Freshet  of  February  10-13,  1886.     Trans.  Am.  Soc.  C.  E.,  Vol. 
25,  p.  253,  1891. 

36.  Talbot,  A.  N.    The  Determination  of  the  Amount  of  Storm  Water.   Proc. 

111.  Soc.  Eng.  &  Surveyors.     1892. 


196  Run-Off. 

37.  Fitzgerald,  Desmond.     Flow  of  Streams  and   Storage  in  Massachusetts. 

Trans.  Am.  Soc.  C.  E.,  Vol.  27,  p.  253.     1892. 

38.  Fitzgerald,  Desmond.     Rainfall,  Flow  of  Streams,  and  Storage.     Trans. 

Am.  Soc.  C.  E.,  Vol.  27,  p.  304,  1892. 

39.  Babb,  C.  C.     Hydrography  of  the  Potomac  Basin.     Trans.  Am.   Soc.  C. 

E.,  Vol.  27,  p.  21,  1892. 

40.  Babb,  C.  C.    Rainfall  and  Flow  of  Streams.    Trans.  Am.  Soc.  C.  E.,  Vol. 

28,  p.  323,  1893. 

41.  Mead,  D.  W.    The  Hydrogeology  of  the  Upper  Mississippi  Valley,  and  of 

Some  of  the  Adjoining  Territory.     Jour.  Ass'n  Eng.   Soc.,  Vol. 
13,  p.  329,  1894. 

42.  Report  on  Water  Supply  of  New  Jersey.     Geol.  Survey  of  N.  J.,  Vol.  3. 

1894. 

43.  Starling,  Wm.     Measurements  of  Stream  Flow  Discharge  of  the  Missis- 

sippi River.    Trans.  Am.  Soc.  C.  E.,  Vol.  34,  pp.  347-492,  1895. 

44.  McLeod,  C.  H.     Stream  Measurements.     The  Discharge  of  St.  Lawrence 

River.     Trans.  Can.  Soc.  C.  E.    June,  1896. 

45.  Data  Relating  to  the  Upper  Mississippi.     Report,  Chief  of  Engineers,  U. 

S.  A.,  1896,  p.  1843. 

46.  Wegmann,  Edward.     The  Water  Supply  of  the  City  of  New  York.     Data 

Relating  to  the  Croton.    Wiley  &  Sons.     1896. 

47.  Johnson,  T.  T.     Data  Pertaining  to  Rainfall   and   Stream   Flow.     Jour. 

Wes.  Soc.  Eng.,  Vol.  1,  p.  297,  June,  1896. 

48.  Chamier,   Geo.     Capacities   Required   for  Culverts   and   Flood   Openings. 

Proc.  Inst.  C.  E.,  Vol.  134,  p.  313.     1898. 

49.  Pannalee,  W.  C.     The  Rainfall  and  Run-off  in  Relation  to  Sewage  Prob- 

lems.    Jour.  Asso.  Eng.  Soc.,  Vol.  20,  p.  204,  Mch.,  1898. 

50.  Seddon,  J.  A.     A  Mathematical  Analysis  of  the  Influence  of  Reservoirs 

upon  Stream  Flow.    Trans.  Am.  Soc.  C.  E.,  Vol.  40,  p.  401.   1898. 

51.  Sherman,  C.  W.    Run-off  of  the  Sudbury  River  Drainage  Area,  1875-1899, 

inclusive.    Eng.  News,  1901. 

52.  Clark,  E.  W.     Storm  Flow  from  City  Areas,  and  Their  Calculation.    Eng. 

News,  Vol.  48,  p.  386,  Nov.  6th,  1902. 

53.  Pence,  W.  D.     Waterways!  for  Culverts.     Proc.  Purdue  Soc.  C.  E.,  1903. 

54.  Weber,  W.  O.    Rainfall  and  Run-off  of  New  England  Atlantic  Coast  and 

Southwestern   Colorado   Streams,  with  Discussion.     Jour.  Asso. 
Eng.  Soc.    Nov.,  1903. 

55.  Abbott,   H.   L.     -Disposition   of  Rainfall    in   the   Basjn    of   the    Chagres. 

Monthly  Weather  Review,  Feb.,  1904. 

56.  Mead,  D.  W.     Report  on  the  Water  Power  of  the  Rock  River.     Chicago, 

1904.     Published  by  the  Author. 

FLOODS. 

57.  The  Flood  in  the  Chemung  River.     Report  State  Engineer,  N.  Y.,  1894, 

p.  387. 

58.  The  Floods  of  February  6th,  1896.     Geol.  Survey  of  N.  J.     1896,  p.  257. 

59.  Morrill,  Park.     Floods  of  the  Mississippi  River.     Bui.  E.,  U.  S.  Dept.  of 

Agric.     1897. 


Literature.  197 


60.  Starling,  Wm.     The  Floods  of  the  Mississippi  River.     Eng.  News,  Vol. 

37,  p.  242.     Apr.  22nd,  1897. 

61.  Starling,  Wm.     The  Mississippi  Flood  of  1897.     Eng  News,  Vol.  38,  p.  2, 

July  1st,  1897. 

62.  McGee,  W.  J.     The  Lessons  of  Galveston.     Nat.  Geo.  Mag.  Oct.,  1900. 

63.  Study  of  the  Southern  River  Floods  of  May  and  June,  1901.     Eng.  News, 

Vol.  48,  p.  102.     Aug.  7th,  1902. 

64.  Brown,  L.  W.     The  Increased  Elevation  of  Floods  in  the  Lower  Missis- 

sippi River.     Jour.  Asso.  Eng.  Soc.,  Vol.  26,  p.  345,  1901. 

65.  Holister,  G.  B.  and  Leighton,  M.  O.     The  Passaic  Flood  of  1902.     Water 

Supply  and  Irrigation  Paper  No.  88,  U.  S.  G.  S, 

66.  Leighton,  M.  O.     The  Passaic  Flood  of  1903.    Water  Supply  and  Irriga- 

tion Paper  No.  92,  U.  S.  G.  S. 

67.  Murphy,  E.  C.     Destructive  Floods  in  the  United  States  in  1903.     Water 

Supply  and  Irrigation  Paper  No.  96,  U.  S.  G.  S. 

68.  Frankenfield,  H.  C.     The  Floods  of  the  Spring  of  1903  in  the  Mississippi 

Watershed.     Bui.  M.,  U.  S.  Dept.  of  Agric.  1903. 

69.  Flood  Damages  to  Bridges  at  Paterson,  N.  J.    Eng.  News,  Vol.  50,  p.  377, 

Oct.  29th,  1903. 

70.  Kansas  City  Flood  of  1903.     Eng.  News,  Vol.  50,  p.  233,  Sept.  17th,  1903. 

71.  Engineering  Aspect  of  the  Kansas  City  Floods.     Eng.  Rec.,  Vol.  48,  p. 

300,  Sept.  12th,  1903. 

72.  Murphy,  E.  C.     Destructive  Floods  in  the  United  States  in  1904.     Water 

Supply  and  Irrigation  Paper  No.  147,  U.  S.  G.  S, 

FORESTS  IN  RELATION  TO  RAINFALL  AND   STREAM  FLOW. 

73.  Swain,  Geo.  F.    The  Influence  of  Forests  Upon  Me  Rainfall  and  Upon  the 

Flow  of  Streams.     Jour.  New  Eng.  W.  Wks.  Ass'n. 

74.  Rafter,  Geo.  W.     Data  of  Stream  Flow  in  Relation  to  Forests.     Ass'n 

C.  E.,  Cornell  Univ.,  Vol.  7,  p.  22,  1899. 

75.  Thompson,   D.    D.     Influence    of   Forests   on   Water   Courses.     Scientific 

American  Sup.  No.  807. 

76.  Vermeule,  C.  C.    New  Jersey  Forests  and  Their  Relation  to  Water  Sup- 

ply. Abstract  of  Paper  Before  Meeting  of  The  American  For- 
estry Ass'n.  New  Jersey,  June  25th,  1900;  Eng.  News,  July  26th, 
1900;  Eng.  Record,  Vol.  42,  p.  8,  July  7th,  1900. 

77.  Bremner.     Water  Ways  for  Culverts  and  Bridges.    Jour.  West.  Soc.  Engrs., 

Vol.  11,  p.  137.     April,  1906. 


CHAPTER  X. 

STREAM  FLOW. 

103.  Flow  in  Open  Channels.  —  The  discussion  of  the  flow  of  water 
in  open  channels  in  Chapter  III  includes  only  such  channels  as 
have  uniform  cross  sections,  alignment,  and  gradient  and  a  bed  of 
uniform  character  throughout  the  length  considered.  Such  condi- 
tions are  closely  approximated  in  artificial  channels  in  which  the 
quantity  of  water  flowing  is  under  control.  In  such  channels,  and 
with  a  steady  flow,  —  that  is  with  the  same  quantity  of  water  passing 

every  cross  section  in  the  same  time,  —  it  is  shown  that: 

/ 

(1)  v  =  c  A/ah  =  c  T/rs"    and  that 


(2)  q  =  av  =  ac  A        =  ac  l/rs" 

v 

In  natural  water  courses  no  two  cross  sections  are  the  same  but 
may  differ  in  area,  a,  and  wetted  perimeter,  p  ;  and  the  fall,  h,  in  any 
length,  1,  usually  differs  considerably  from  reach  to  reach.  The 
quantity,  q,  of  water  flowing  in  any  such  stream  is  also  constantly 
changing.  There  every  condition  of  uniform  flow  is  lacking  and 
can  only  be  approximated  for  selected  reaches  of  such  streams  and 
during  periods  when  stream  flow  is  fairly  steady. 

104.  Changes  in  Value  of  Factors  with  Changes  in  Flow.  —  From 
an  examination  of  equation  (2)  it  is  evident  that  in  any  channel  as 
the  quantity  of  water  flowing,  q,  changes,  there  must  be  a  corre- 
sponding change  in  some  or  all  of  the  factors  on  the  other  side  of  the 
equation. 

For  steady  flow  in  a  uniform  channel,  s  remains  constant  and  all 
changes  are  confined  to  the  values  of  a,  c  and  r.  The  laws  of 
change  in  the  values  of  c  are  given  by  Kutter's  and  Bazin's  formu- 
las, but  are  best  illustrated  and  understood  by  reference  to  Fig.  22, 
which  is  a  graphic  expression  of  the  formula  of  Bazin. 

In  variable  flow  a  change  in  all  of  the  factors  usually  accompa- 
nies a  chang:e  in  the  value  of  q,  each  factor  changing  in  accordance 
with  the  physical  conditions  of  the  channel. 

The  changes  in  the  value  of  c,  in  an  irregular  channel,  do  not  al- 
ways seem  to  follow  Bazin's  law.  In  some  cases  c  is  even  found  to 


Flow  in  Open  Channels. 


199 


decrease  as  r  increases.  The  law  of  simultaneous  increase  in  c  and 
r  presupposes  a  channel  of  uniform  character  and  condition.  If  an 
increase  in  the  hydraulic  radius,  r,  in  any  channel  is  accompanied  by 
a  radical  change  in  the  character  of  its  bed  the  law  will  not  hold. 
It  is  evident  that  under  such  conditions  the  values  of  c  for  different 
values  of  r  are  not  fairly  comparative.  No  more  uniform  law  of 
change  can  be  expected  under  such  conditions  than  would  occur  in 
the  comparison  of  the  relation  of  c  and  r  for  entirely  different  chan- 
nel sections. 

In  Fig.  .TOO  are  shown  the  observed  values  of  c  and  r  for  certain 
reaches  of  the  Wisconsin  River  above  Kilbourn,  Wis.     It  will  be 


10        20        30        40        SO         6O        70        80        90        100      110       120 


Pig.  100.— Relations  of  Coefficient  to  Hydraulic  Radius  in  Certain  Reaches 

of  the  Wisconsin  River. 


200 


Stream  Flow. 


noted  that  the  value  for  readies  A,  D  and  E  follow  in  general  the 
law  as  established  by  Bazin.  These  are  fairly  uniform.  On  the 
other  hand  the  values  of  c  and  r  for  reaches  b  and  c  seem  to  follow 
an  entirely  different  law,  a  condition  due  to  irregularities  in  the 
cross  section  of  the  reach. 

Where  the  values  of  a,  p  and  r  vary  radically  from  section  to  sec- 
tion and  differ  materially  from  the  values  in  the  sections  considered 
and  on  which  calculations  are  based,  the  value  of  c  will  be  found  to 
differ  radically  from  that  which  the  character  of  the  bed  and  the  en- 
tire section  would  indicate.  Absurd  values  of  c  are  a  clear  indica- 
tion that  the  sections  selected  are  not  representative.  The  calcu- 
lated value  of  c  is  modified  by  all  unknown  or  unconsidered  factors 
of  the  reach.  The  influences  of  irregularities  in  bed  or  section,  the 
presence  of  unconsidered  bends  or  changes  in  the  gradient,  and  all 
other  irregularities  in  the  channels,  modify  the  values  of  c. 

105.  Effects  of  Variable  Flow  on  the  Hydraulic  Gradient. — In 
order  to  understand  the  effect  of  variable  flow  on  the  surface  gradi- 
ent of  a  stream,  and  in  order  to  realize  how  conclusions  drawn  from 
the  laws  of  uniform  flow  must  be  modified  to  meet  conditions  found 
in  natural  streams,  it  is  necessary  to  consider  the  cause  of  variable 
flow  in  a  stream,  the  variation  in  channel  conditions,  and  both  the 
effect  of  flow  on  such  conditions  and  the  effect  of  such  conditions  on 
the  flow  of  a  stream. 


Tnic^t  by  Time  Fti 


REPRODUCTION  OF  RECORD  OF  U.  S.L.S.  GAUGE.  No.  5  FOR  MAY  17,  1609. 

He  AD  OF  <ST:CLAin  ft/vcn. 
«  7  a  e  10  u  "i?*          ia  14 


7r*(eStr  TTme  ft/id fs. 


Fig.  101.— Variations  in  Gauge  Height  of  the  St.  Clair  River. 


Effects  of  a  rising  or  a  Falling  Stream  on  Gradient.         201 

The  surface  of  a  stream  is  constantly  fluctuating,  not  oaily  on  ac- 
count of  the  variation  in  flow,  but  also  on  account  of  wind,  baro- 
metric pressure  and  changes  in  the  hydraulic  gradient.  Such 
changes  occur  from  hour  to  hour,  and  even  from  minute  to  min- 
ute. Larger  rivers,  fed  directly  by  great  lakes,  are  more  sus- 
ceptible to  these  changes  on  account  of  the  broad  lake  area,  giving 
wind  and  barometric  pressure  greater  opportunity  to  act.  Every 
stream  is,  however,  more  or  less  susceptible  to  these  changes,  and 
gauge  readings  taken  daily,  therefore,  show  only  in  an  approximate 
way  the  true  height  of  the  surface  of  the  river  at  the  point  of  ob- 
servation. This  is  well  shown  by  Fig.  101,  which  is  reproduced 
from  the  autographic  record  of  a  gauge  at  the  head  of  the  St.  Claire 
River. 

106.  Effects  of  a  Rising  or  a  Falling  Stream  on  Gradient. — In  a 
channel  of  uniform  section,  the  bed  of  the  channel  AB  (see  diagram 
A,  Fig.  102)  having  a  uniform  slope,  all  cross  sections,  such  as  Aa 
and  Bb,  will  be  alike  and  the  wetted  perimeters  and  the  hydraulic 
radii  will  be  identical  for  all  sections.  The  fall,  bx,  will  be  uniform 
in  all  equal  lengths,  1,  of  the  channel,  and  such  uniform  conditions 
will  be  maintained  for  all  regular  discharges  after  regular  flow  is 
once  established. 

In  such  channels,  during  changes  in  the  stages  of  flow,  the  hy- 
draulic gradient  or  slope  will  change  until  uniform  flotw  is  estab- 
lished. In  all  cases  illustrated  in  Figs.  102  and  103,  the  line  ab  rep- 
resents the  hydraulic  gradient  which  will  obtain  if  uniform  flow  is 
maintained  in  the  channel  and  if  there  be  no  change  in  the  channel 
section  or  other  conditions^  The  actual  water  surface,  caused  by 
variable  flow,  is  in  each  case  shown  by  the  line  a'b.  In  each  case,  the 
fall,  bx,  would  be  necessary  to  produce  uniform  flow  from  A  to  B 
and  to  assure  the  flow  of  the  normal  quantity  of  water  passing  the 
section  Bb  as  in  diagram  A.  In  diagram  B  and  C,  Fig.  102,  the  con- 
ditions of  variable  flow  in  a  uniform  channel  are  graphically  repre- 
sented. The  actual  flow  is  greater  or  less  than  the  normal  quantity, 
according  as  the  gradient  is  increased  or  diminished. 

In  diagram  B,  the  conditions  with  a  rising  stream  are  shown. 
Under  these  conditions  the  quantity  of  water  passing  the  section 
Aa  is  greater  than  the  quantity  passing  the  section  Bb,  by  the  quan- 
tity of  water  necessary  to  fill  up  the  channel  of  the  stream  to  a  new 
and  uniform  surface  gradient.  The  head  needed  to  produce  the  flow 
past  the  section,  Aa,  is  represented  by  the  height,  xx'.  The  total 
fall  between  A  and  B  is  therefore  greater  than  that  required  for  the 

12 


202 


Stream  Flow. 


H 

Fig.  102. — Effects  of  Variable  Flow  on  the  Hydraulic  Gradient  of  a  Stream. 


Effects  of  Channel  Conditions  on  Gradient.  203 

uniform  flow  as  represented  by  the  head  bx'.  This  produces  not 
only  a  greater  flow  at  Aa,  but  also  a  flow  greater  than  would  be  nor- 
mal at  section  Bb. 

In  diagram  C,  Fig.  102,  the  conditions  of  a  falling  stream  are  rep- 
resented. In  this  case,  the  head  at  section  Bb  at  the  moment  of 
observation  would,  if  the  flow  was  uniform,  produce  a  normal  flow 
which  would  require  the  fall,  bx,  to  maintain  it.  With  a  falling 
stream,  the  section  AB  is  emptying  and  the  quantity  of  water  pass- 
ing the  sectian  Aa  is  less  than  the  quantity  of  water  passing  the 
section  Bb,  which  in  turn  is  also  less  than  the  normal  flow 'for  the 
existing  head.  A  less  fall  is  therefore  required  to  produce  the  flow 
passing  Bb,  which,  with  the  lower  slope  and  the  same  cross  section, 
is  less  in  quantity  than  would  be  the  case  under  conditions  of  uni- 
form flow.  This  fall  is  represented  by  the  height,  bx',  which  is  less 
than  the  height  bx,  required  for  uniform  flow  by  the  height  xx': 
consequently  the  slope  of  the  river  is  a'b. 

From  the  above  considerations  it  will  be  seen  (see  diagram  D, 
Fig.  102)  that  a  given  gauge  height,  Bb,  may  not  always  represent 
the  same  flow,  for  the  discharge,  Q,  is  a  function  not  only  of  the 
cross  section,  a,  but  also  of  the  slope,  s.  A  single  gauge  height  may 
therefore  represent  a  considerable  range  of  flows  depending  on  the 
hydraulic  gradient  which  may  pass  through  the  point  with  a  uni- 
form, a  rising  or  a  falling  stream.  It  is  obvio'us  that  the  flows  rep- 
resented by  the  hydraulic  gradient,  a'  be',  abc  and  a"bc",  while  pro- 
ducing the  same  gauge  height  at  Bb,  nevertheless  represent  three 
different  conditions  of  flow. 

In  the  establishment  of  the  relations  between  gauge  heights  and 
flow,  it  is  therefore  important  that  the  observed  flow  corresponding 
to  a  given  gauge  reading  be  taken  during  a  period  of  essentially  uni- 
form flow,  for,  from  the  above  considerations,  it  will  be  seen  that 
any  determination  or  observation  made  with  a  rising  or  a  falling 
stream  must  necessarily  be  more  or  less  in  error.  It  will  also  follow 
that, .after  a  rating  curve  and  rating  table  have  been  established, 
the  gauge  height  taken  during  changes  in  the  conditions  of  flow  will 
be  more  or  less  in  error,  although  such  errors  will  equalize  to  a  con- 
siderable extent  and  will,  in  the  main,  prove  unimportant. 

107.  Effects  of  Channel  Condition  on  Gradient. — The  flow  of 
water  in  a  natural  channel  is  far  from  being  uniform  and  it  is  im- 
portant for  the  engineer  to  realize  this  lack  of  uniformity  and  the 
effect  of  such  conditions  upon  the  flow  of  the  stream.  In  any  chan- 
nel of  uniform  gradient,  as  AB  in  diagram  E  (Fig.  102),  if  at  the 


204 


Stream  Flow. 


B' 


Fig.  103. — Effects  of  Channel  Grade  and  of  Obstruction  on  the  Hydraulic 

Gradient  of  a  Stream. 

section  Bb  the  coefficient  c  is  decreased  on  account  of  increased 
roughness  in  the  bed  of  the  stream,  or  if  the  area  of  the  channel,  a, 
is  contracted,  a  change  in  the  hydraulic  gradient  will  follow.  The 
normal  gradient  with  uniform  flow  would  take  the  position  ab,  but 
on  accoamt  of  the  change  in  conditions  at  Bb,  the  depth  must  in- 
crease to  keep  q  a  constant ;  a  must  increase  to  offset  the  decrease  in 
c  or  c  must  increase  to  offset  the  decrease  in  a  if  q  remains  constant. 
The  surface  must  therefore  rise  to  the  point  x  and  a  new  hydraulic 


Effect  of  Change  in  Grade.  2o5 

gradient  will  be  established  and  maintained  until  other  changes  in 
the  channel  condition  again  modify  the  same.  Between  the  new  and 
old  gradients,  a  transition  curve  will  be  established  extending  both 
above  and  below  the  point  at  which  the  change  in  condition  takes 
place  to  some  point,  y,  frequently  a  long  distance  upstream. 

The  opposite  condition  is  shown  by  diagram  F,  Fig.  102.  In  this 
diagram  the  effect  of  an  increase  in  the  coefficient,  c,  of  the  bed  or 
in  the  area,  a,  of  the  stream  is  represented.  If  c  increases,  a  less 
section  will  be  required  below  that  point  and  again  the  surface  is 
lowered;  or  if  the  width  of  the  stream  increases,  the  depth  will 
diminish  in  order  that  ca  may  remain  constant. 

Variable  flow  is  also  caused  by  a  sudden  enlargement  in  the 
river  section  or  by  a  discharge  of  the  stream  into  a  larger  stream  or 
into  a  lake  or  pond.  Such  conditions  are  shown  by  diagrams  G 
and  H,  Fig.  102.  The  character  of  the  transition  curve  in  such 
cases  will  depend  on  the  height  of  the  surface  of  the  water  into 
which  the  stream  is  discharged.  If  the  water  surface  of  the  lake 
is  above  b,  the  curve  will  be  concave  upward  (see  diagram  G)  and 
if  the  surface  is  below  b,  the  curvature  will  be  doiwnward  (see  dia- 
gram H). 

108.  Effect  of  Change  in  Grade  and  of  Obstructions. — Variable 
flow  may  also  be  caused  by  changes  in  the  slope  of  the  stream  bed 
as  shown  by  diagrams  A  and  B,  Fig.  103.  The  area  of  the  stream 
must  increase  as  the  bed  slope  is  decreased,  or  must  decrease  as 
the  slope  of  the  bed  is  increased  in  order  to  fulfill  the  conditions  of 
equation  (2). 

It  is  evident  that  uniform  slope  may  be  maintained  even  with 
changed  conditions  if  the  changes  that  occur  give  rise  to  equal  and 
opposite  effects.  For  example,  uniform  slope  may  be  maintained 
if  the  area  of  section  a  is  reduced  and  the  coefficient  c  is  increased 
to  such  an  extent  that  the  product  ac  remains  constant  at  each  sec- 
tion of  the  channel. 

Variable  flow  is  also  caused  by  the  passage  of  the  stream  over 
weirs  or  dams  and  the  effect  on  the  gradient  will  vary  as  shown  by 
diagram  C  and  D,  Fig.  103.  Variations  may  also  be  caused  by  a 
change  in  the  bed  (see  diagram  E,  Fig.  103),  or  by  local  contrac- 
tions, submerged  weirs  or  other  obstructions  as  shown  by  dia- 
gram F,  Fig.  103. 

In  all  of  the  above  described  cases  it  is  obvious  that  if  the  slope 
of  the  stream  is  measured  on  any  of  these  transition  curves,  a  false 
idea  of  slope  will  obtain  and  a  false  relation  will  be  established  for 


206 


Stream  Flow. 


43 
46 
44 
42 
40 
38 
36 
34 
32 
30 
28 
26 
24 
22 
20 
18 


n 


n 


pig. 


15         16         17         18         19         20        21         22       23        24        23 
GAUGE     HEIGHTS     AT     KILBOURN. 

104. — Relations  of  Guage  Heights  at  Various  Stations  on  the  Wiscon- 
sin River. 


Effect  of  Change  in  Grade.  207 

the  condition  of  stream  flow.  It  is  therefore  essential  in  any  meas- 
urement of  a  stream  or  in  the  establishment  of  any  gauging  station 
that  the  location  for  such  observations  be  carefully  selected  on  a 
reach  of  the  stream  where  conditions  of  essentially  uniform  flow 
prevail  and  that  all  observations  be  taken  during  stages  where  the 
flow  of  the  stream  is  practically  constant.  If  gauges  are  established 
at  various  points  along  the  course  of  a  river  and  are  read  simultan- 
eously, and  if  the  flow  is  uniform  and  no  falls,  rapids  or  tributaries 
intervene,  the  same  differences  in  elevation  should  always  obtain 
with  the  same  stage  of  water. 

A  system  of  gauges  as  described  above  was  recently  established 
at  Kilbourn  on  the  Wisconsin  River  in  order  to  determine  the  river 
slopes  near  that  place.  A  large  number  of  practically  simultaneous 
readings  were  taken  in  order  to  determine  the  relations  between  the 
gauge  heights  at  the  various  points  compared  with  the  Kilbourn 
gauge. 

Fig.  104  shows  the  results  of  the  gauge  readings  at  the  various 
stations  compared  with  the  gauge  readings  at  Kilbourn.  It  will 
be  noted  from  the  diagram  that  the  slope  of  the  river  was  far  from 
uniform  at  different  times  during  these  readings,  and,  in  a  number 
of  cases,  the  same  gauge  reading  at  Kilbourn  was  accompanied  by 
readings  at  other  gauges  that  differed  from  each  other  by  more 
than  a  foot.  For  example,  compare  the  gauge  readings  at  Kilbourn 
with  the  readings  at  gauge  No.  5.  With  a  gauge  reading  of  17  ft. 
at  Kilbourn,  the  normal  gauge  reading  at  No.  5  should  be  23  feet, 
and  with  a  normal  flow,  the  fall  between  gauge  No.  5  and  the  Kil- 
bourn gauge  would  be  5  ft.  From  the  diagram  it  will  be  seen  that 
during  a  certain  stage  of  flow  in  the  river  the  gauge  reading  at 
gauge  No.  5,  with  a  17  foot  reading  at  Kilbourn,  was  about  22  J  ft. 
Under  these  conditions  the  fall  between  gauge  No.  5  and  the  Kil- 
bourn gauge  was  only  4^  ft.  The  slope  being  reduced,  the  quantity 
of  water  actually  passing  the  Kilbourn  gauge  under  these  condi- 
tions was  less  than  the  normal  flow  for  the  17  ft.  gauge  height. 
On  two  other  occasions  where  the  gauge  reading  at  Kilbourn  was 
approximately  17  feet,  the  actual  gauge  reading  at  gauge  No.  5  was 
about  24  feet.  During  these  conditions  the  actual  fall  in  the  river 
between  gauge  No.  5  and  the  Kilbourn  gauge  was  5  feet,  or  one 
foot  more  than  normal.  Hence  the  quantity  of  water  flowing  by  the 
Kilbourn  gauge  at  this  time  was  more  than  the  normal  quantity 
indicated  by  the  Kilbourn  gauge. 

Readings  of  other  gauges  compared  with  the  Kilbourn  readings 


208 


Stream  Flow. 


B 


will  show  that  at  certain  times  the  flow 
was  normal  and  at  other  times  the  river 
must  have  been  rising  or  falling  and  that 
consequently  the  gauge  at  Kilbourn  at  the 
time  of  such  reading,  was  not  accurately 
representing  the  quantity  of  water  flow- 
ing by  the  Kilbourn  section.  The  above 
example  taken  of  the  variation  in  slope 
between  the  Kilbourn  gauge  and  gauge 
No.  5  indicated  practically  the  maximum 
abnormal  conditions.  The  actual  varia- 
tion in  flow  at  Kilbourn  during  these  con- 
ditions was  not  determined  and  is  not 
definitely  known. 

109.  Relation  of  Gauge  Heights  to 
Flow. — The  area  of  any  cross  section 
equals  the  product  of  the  height  of  the 
section  into  some  function  of  its  width : 


(3) 


=  h  X  f 


In  a  rectangular  cross  section  f=i,  (see  A,  Fig.  105).  In  a  tri- 
angular section,  f=-5  (see  B,  Fig.  105).  In  all  cases  of  regular  sec- 
tion f  can  be  mathematically  expressed,  and  for  irregular  sections 
(see  C,  Fig.  105)  the  relation  may  be  obtained  by  measurement. 
If  the  height  of  the  surface  is  referred  to  a  gauge  height,  H,  the 
zero  of  the  gauge  may  or  may  not  correspond  with  the  bottom  of 
the  channel.  If  H=the  gauge  height,  then  h=-H-fe,  in  which  e  is 
the  distance  from  the  bottom  of  the  channel  to  the  bottom  of  the 
gauge.  Substituting,  therefore,  the  value  of  h  in  equation  (3)  it 
becomes : 

(4)  a  =  (H  +  e)  X  f  (w)  -  Hf(w)  -f-  ef(w), 
And  substituting  this  value  in  equation  (2)  it  becomes : 

(5)  Q  =  Hf(w)  c  Vn  +  ef( w)  c  l/rs 

With  this  equation,  and  with  the  flow  in  a  fixed  and  uniform  chan- 
nel, if  the  relation  can  be  established  between  r,  s,  c,  e,  w  and  f  for 
each  gauge  height,  H,  the  corresponding  value  of  Q  can  be  deter- 
mined. As  these  relations  are  mathematically  expressed  for  uni- 
form flow  by  the  above  equation,  they  can  also  be  represented 
graphically  by  a  curve  which  will  show  the  relation  between  Q  and 
H  for  all  conditions  of  uniform  flow  that  obtain  in  the  given  chan- 


Relation  of  Gauge  Height  to  Flow. 


209 


•nel.  Such  a  curve  is  called  a  discharge  or  rating  curve.  This  equa- 
tion (5)  can  be  readily  solved  when  f  is  a  regular  variable  and  when 
•c,  r  and  s  can  be  determined.  Where  the  function,  f,  is  an  irregular 
variable,  no  mathematical  solution  is  practicable  but  the  relations 
may  be  determined  experimentally  and  can  be  expressed  by  a  rating 
table  or  graphically  by  a  rating  curve.  Such  a  rating  table  and  curve 
can  be  constructed  for  every  fixed  channel  or  section  of  a  stream 
for  condition  of  uniform  flow,  no  matter  how  irregular  the  section 
•or  how  the  values  of  the  function  of  the  section  may  vary  for  differ- 
ent gauge  heights. 


Discharge  in  Cubic  Feet  per  Second. 
Fig.  10G. — Rating  Curve  for  Wisconsin  River  at  Kilbourn,  Wis. 

Fig.  106  shows  a  rating  curve  established  for  the  Wisconsin  River 
•at  Kilbourn,  Wis.  The  small  circles  show  the  flow  relative  to  gauge 
'height  at  the  time  the  observations  were  made.  They  were  care- 
fully made  in  a  fairly  satisfactory  section  and  fall  fairly  well  on  a 
smooth  curve  drawn  from  this  data  to  represent  the  relation  of 
gauge  height  to  flow  at  similar  or  intervening  heights. 

The  character  of  the  rating  curve  for  regular  and  irregular  sec- 
tions is  shown  by  Fig.  45,  page  95.  Whenever  the  section  remains 


2IO 


Stream  Flow. 


similar  for  different  gauge  heights,  the  rating  curve  will  be  a  smooth 
curve,  but  when  irregularities  occur  in  the  section,  the  curve  be- 
comes broken  more  or  less  according  to  the  extent  of  the  irregu- 
larity. 

It  has  already  been  pointed  out  that  any  change  in  the  cross  sec- 
tion of  the  stream  after  a  rating  curve  has  been  established  will 
necessitate  the  establishment  of  a  new  curve.  The  variation  in  rat- 
ing curves  under  variation  in  channel  conditions  is  shown  in  Fig.  46, 
page  96. 


1234587 

Fig.    107. — Variations    in    the    Cross-section    of    the    Missouri    River    near 

Omaha,  Neb.* 

The  actual  change  in  channel  conditions  that  affects  the  relation 
of  head  and  flow  is  well  illustrated  by  Fig.  107  which  shows  the 
changes  that  actually  took  place  in  the  cross  section  of  the  Missouri 
River  near  Omaha,  Nebraska. 

no.  Variations  in  Velocity  in  the  Cross-section  of  a  Stream. — 
The  velocity  of  flow  of  a  stream  varies  greatly  at  different  points  in 
any  cross  section.  In  any  channel  the  friction  of  the  sides  and  bed 
reduces  the  velocity  of  that  portion  of  the  stream  in  contact  and 
adjacent  to  them.  If  the  bed  at  different  points  of  the  cross-section 
is  not  uniform,  as  is  always  the  case  in  the  beds  of  natural  streams, 
the  retarding  effects  on  different  portions  of  the  stream  varies,  and 
a  consequent  variation  in  velocity  results.  The  distribution  of  the 
velocities  in  the  cross  section  of  the  St.  Clair  River  is  shown  in  Fig. 
108,  both  by  lines  of  equal  velocity  and  by  figures  giving  the  ve- 
locity as  actually  measured.  In  this  figure  the  effect  of  the  friction 

*Todd.  Bull.  158  U.  S.  Geol.  Surv. 


Variation  in  Velocity  in  the  Cross-Section  of  a  Stream.      211 


Curves  of  Equal  Velocity 
Section  Dm  Dock 


Mean  Wafer  Stage  - 
Mean  Velocity        -3.33  t 


STATIONS.    I          1          3 


Fig.    108. 


S>         K>         nf       g         13 


Transverse  Curve  of  Mean  Velocities 
'Section  'Dry  Dock' 

Mean  Hbter'ttyi-5766 


Fig.  109. 


I        2       3       4        5       6       7       8       9       10     II       12      13     14      15     16     17      IB     19    20    2> 


5FT 
10- 
15" 
20- 
25- 
30- 
35- 


\/ 


Fig.  110.— Vertical  Velocity  Curves,  Section  Dry  Dock. 


212 


Stream  Flow. 


of  the  bed  and  banks  is  clearly  shown. 
The  friction  between  the  stream  sur- 
face and  the  atmosphere  is  also 
shown  by  the  fact  that  the  maximum 
velocity  is  not  at  the  surface  but  is  a 
short  distance  below  the  surface. 
The  surface  velocity  may  be  modified 
radically  by  the  direction  and  velocity 
of  the  wind. 

Fig.  109  shows  the  transverse 
curve  of  mean  velocities  in  this  sec- 
tion. The  distribution  of  velocities 
in  each  vertical  section  is  shown  in 
Fig.  no.  The  velocities  here  shown 
are  relative  only  as  compared  with 
each  vertical.  The  velocity  at  the 
bottom  of  each  curve  is  that  shown 
by  figures  in  Fig.  108. 

The  distribution  of  velocities  in 
any  section  is  not  the  same  under  all 
conditions  of  flow  but  differs  mater- 
ially with  the  stage  of  the  river.  This 
is  illustrated  by  Fig.  in  in  which  is 
shown  three  sections  of  the  same 
stream  illustrating  conditions  of  low, 
medium  and  high  water.  Above  each 
section  is  shown  a  corresponding 
transverse  curve  of  mean  velocities 
of  flow.  The  change  in  the  distribu- 
tion of  velocities  as  the  stream  in- 
creases should  be  noted. 

The  distribution  of  velocity  is  also 
affected  by  bends  in  the  stream  above 
the  point  of  observation  which  tends 
to  throw  the  current  of  the  stream 
toward  the  concave  side,  and  to  cause 
a  transverse  slope  in  the  section  of 
the  stream  at  the  curve.     Such  a  condition  (see  Fig.  112)   creates 
cross  currents  and  eddies  and  produces  conditions  of  variable  flow. 
From  Fig.  108  it  will  be  seen  that  in  any  vertical  line  in  a  given 
section,  the  velocities  will  vary  with  the  condition  of  the  bed,  and 


Variation  in  Velocity  in  the  Cross-Section  of  a  Stream.     213 


Fig.   112. 

CALM  WIND  DOWN  STREAM         WIND,  UP  STREAM        ICE  COVERED 


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Fig.  113.— Ideal  Vertical  Velocity  Curves. 


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Stream  Flow. 


the  influence  of  air  current  or  ice  at  the  surface.  These  conditions 
have  an  influence  on  the  velocities  in  each  section  considered.  Vari- 
ations in  the  vertical  velocities  can  be  better  studied  by  means  of  the 
vertical  velocity  curve,  which  can  be  obtained  by  means  of  velocity 
observations  taken  in  a  vertical  line  from  the  surface  to  the  bed  of 
the  stream.  Ideal  curves  under  various  conditions  are  illustrated  by 
Fig.  113.  Figs.  114,  115  and  116  are  reproduced  from  the  report  of 
the  State  Engineer  of  New  York  for  the  year  1902.  These  diagrams 
show  comparisons  between  the  mean  vertical  velocities  of  streams 
having  different  classes  of  beds.  From  these  illustrations  it  will  be 
noted  that  there  is  a  general  similarity  between  the  various  velocity 
curves  which  aids  materially  in  the  measurement  of  stream  flow.  It 
will  be  noted,  for  example,  that  the  mean  velocity,  in  any  vertical 
velocity  curve  from  an  open  channel,  lies  near  the  point  of  .6  total 
depth  but  that  with  varying  conditions  this  position  may  vary  from 
55  per  cent,  to  about  75  per  cent,  of  the  depth.  The  velocity  at  .6 
depth  is  found  to  average  nearly  100  per  cent  of  the  mean  velocity, 
but  may  actually  vary  from  95  per  cent,  to  105  per  cent,  of  the  mean 


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Fig.  115. — Mean  Vertical  Velocity  Curves. 


Effects  of  Ice-Covering  on  the  Distribution  of  Velocites.    215 


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PER     CENT    OF    MEAN     VELOCITY 

Fig.  116. — Mean  Vertical  Velocity  Curves. 

velocity.  The  velocity  at  the  surface  is  subject  to  the  external  influ- 
ence of  atmospheric  currents  and  is  not  so  constant  in  its  relation  to 
the  mean  velocity.  The  surface  velocity  will  average  about  no  per 
•cent  of  the  mean  velocity  of  the  vertical  curve,  but  is  found  to  vary 
with  the  variations  in  conditions  from  105  per  cent,  to  130  per  cent. 
of  such  velocity. 

in.  Effects  of  Ice-Covering  on  the  Distribution  of  Velocities.— 
The  effect  of  the  formation  of  an  ice  sheet  over  a  stream  is  to  ma- 
terially increase  the  surface  friction  and  results  in  a  rearrangement 
of  velocities  in  the  cross  section.  As  the  ice  sheets  form  in  winter, 
the  conditions  will  vary  from  that  of  an  open  stream  to  that  of  a 
closed  channel.  The  velocities  are  gradually  affected  as  the  ice  be- 
gins to  form,  until  the  entire  surface  is  affected  where  the  stream 
becomes  entirely  covered.  As  the  ice  sheet  thickens  more  of  the 
cross  section  of  the  stream  is  occupied  by  the  ice  sheet,  and  greater 
friction  results.  Fig.  117  shows  two  vertical  velocity  curves,  one  for 
an  open  and  one  for  an  ice-covered  channel.  These  may  be  regarded 


2l6 


Stream  Flow. 


0 
10 
20 
30 


60 
Id 
O 

a  70 
u 

a 

80 
90 


MEAN   OF    4   CURVES  -OPEN  SECTION. 


---  MEAN  OF  1  3  CURVES  -  UNDER   ICE. 


40         50 


120         130 


140- 


60          70  80          90          100         NO 

PER    CENT     OF    MEAN    VELOCITY 

Fig.  117. — Comparative   Mean  Vertical  Velocity   Curves   for  Open   and  Ice 

Covered  Section. 

as  typical  of  open  and  closed  conditions  between  which  the  actual 
velocities  wall  vary  with  the  conditions  of  the  ice. 

The  change  in  the  distribution  of  velocities  results  in  an  entire 
change  in  the  relation  between  gauge  height  and  flow  so  that  the 
rating  curve  for  an  open  section  will  not  apply  to  the  river  under 
ice  conditions. 

If  therefore  the  stream  flow  is  to  be  accurately  determined  during 
such  condition,  it  becomes  necessary  to  establish  the  new  relation 
between  gauge  height  and  flow. 

As  before  noted,  such  relations  vary  somewhat  with  the  condi- 
tions of  the  ice  sheet  but  may  be  regarded  as  fairly  constant  when! 
the  section  is  fairly  clear  and  deep.  The  relations  between  the  rat- 
ing curves  for  this  open  channel  and  for  ice  conditions  as  deter- 
mined by  the  United  States  Geological  Survey  for  the  Wallkill 
River  at  Neupaltz,  N.  Y.  is  shown  in  Fig.  118. 

Table  XXI,  from  an  article  by  F.  A.  Tillinghast  (sec  Engineer- 
ing News,  May  nth,  1905),  shows  the  relations  of  maximum  and 


Effects  of  Ice-Covering  on  Velocities. 


217 


o>   14 

1 

iu 

1  12 

Ul 

o 

2 

10 
8 


EOQO 


4000  6000  8000 

DISCKAB3E    IN    CUBIC    FEET     PER     SECOND. 


10000 


Fig.  118. — Rating  Curve  for  Wallkill  River  at  Newpaltz,  N.  Y. 

mean  velocities  in  the  verticals.  •  It  should!  be  noted  that  there  are 
two  points  of  mean  velocity  under  ice  conditions  that  average  n 
per  cent,  and  71  per  cent,  of  the  total  depth  below  the  Surface.  The 
point  of  maximum  velocity  is  at  an  average  depth  of  36  per  cent,  of 
the  total  depth  of  the  stream  and  averages  IIQ  per  cent,  of  the  mean 
velocity; 

TABLE  XXI. 
Position  o/  Mean  and  Maximum  Velocities  in  a  Vertical  Plane  Under  Ice. 


Coeffi- 

Depth 

Stream  and  Place 

Depth  from 
Under  Sur- 
face of  Ice 
Feet 

Num- 
ber of 
curves 

Depth  of 
Mean 
Velocity 

of 
Maxi- 
mum 
Veloc- 

to  re- 
duce 
Max. 

tn 

ity 

Mean 

Wallkill  at  Neupaltz,  N.  Y.  .  .  .  (a) 
Wallkill  at  Neupaltz,  N.  Y.  .  .  .  (b) 
Esopus  at  Kingston,  N.  Y  (a) 
Esopus  at  Kingston,  N.  Y  (b) 
Rondout  at  Rosendale,  N.  Y.  .  .  (a) 
Rondout  at  Rosendale,  N.  Y.  .  .  (b) 
Connecticut  at  Urford,  N.  H.  .  .(c) 

4  to  12 
4  to  19 
2.3  to  7.4 
5  to  8 
4  to  8 
5to7 
2.5  to7.7 

20 
26 
16 
8 
5 
8 
18 

0.12 
0.13 
0.08 
0.11 
0.08 
0.13 
0.11 
0.11 

0.71 
0.74 
0.68 
0.73 
0.68 
0.21 
0.69 
0.71 

0.38 
0.38 
0.36 
0.37 
0.35 
0.35 
0.35 
0.36 

0.85 
0.86 
0.80 
0.85 
0.82 
0.86 
0.85 
0.84 

Notes:  a.  By  F.  H.  Tillinghast. 

b.  By  W.  W.  Schlecht. 

c.  By  C.  A.  Holden. 

13 


CHAPTER  XI. 

THE  MEASUREMENT  OF  STREAM  FLOW. 

112.  Necessity  for  Stream  Flow  Measurements. — In  order  to 
ascertain  the  value  of  a  stream  for  water  power  purposes,  it  is  neces- 
sary to  determine  the  amount  and  variations  in  its  continuous  flow 
either  by  comparison  with  the  flow  of  other  streams  or  by  the  direct 
observation  of  the  flow  of  the  stream  itself.  As  has  already  been 
shown,  the  latter  method  is  by  far  the  most  satisfactory  as  the  de- 
termination of  the  actual  flow  of  the  stream  eliminates  all  errors  of 
comparison,  and  the  necessity  for  any  allowances  or  modifications 
on  account  of  differences  in  geological,  geographical,  topographical 
or  meteorological  conditions  on  the  drainage  area. 

The  Hydrographic  Division  of  the  United  States  Geological  Sur- 
vey has  undertaken  the  gauging  of  a  large  number  of  streams  in  the 
United  States  and  has  established  numerous  gauging  stations  at 
which  observations  have  been  made  for  a  number  of  years.  This 
data,  references  to  which  are  given  in  the  list  of  literature  appended 
to  Chapter  IX,  is  of  great  value  for  comparative  purposes.  It  is 
seldom,  however,  that,  when  a  stream  is  to  be  investigated  for  water 
power  purposes,  flow  data,  at  the  particular  point  under  consider- 
ation, is  available.  One  of  the  first  duties  of  the  engineer,  there- 
fore, usually  consists  in  making  measurements  of  the  stream  flow 
and  establishing  stations  at  which  the  daily  flow  can  be  observed 
and  recorded. 

The  methods  in  use  by  the  United  States  Geological  Survey  are 
the  result  of  much  study  and  investigation  and  probably  represent 
the  most  practical  methods  for  making  such  observations  with  a  fair 
degree  of  accuracy.  Many  of  the  methods  and  suggestions  in  this 
chapter  are  based  on  the  methods  and  conclusions  of  the  Survey  as 
modified  by  the  experience  and  practice  of  the  writer.* 

*  These  methods  are  described  in  detail  in  Water  Supply  and  Irrigation 
Papers  No  94,  entitled,  "Hydrographic  Manual  of  the  United  States  Geologi- 
cal Survey,"  and  No.  95,  entitled  "Accuracy  of  Stream  Measurements."  See 
also  "River  Discharge"  by  J.  C.  Hoyt  and  N.  C.  Grover, — John  Wiley  and 
Sons,  1907. 


Methods  for  the  Determination  of  Flow.  219 

113.  Methods  for   the   Estimate  or   Determination   of   Flow   in 
Open  Channels. — There  are  three  general  methods  of  estimating  or 
determining  the  flow  of  water  in  streams  with  open  channels. 

First — By  the  measurement  of  the  cross  section  and  slope  and  the 
calculation  of  flow  by  Chezy's  formula,  together  with  Kutter's  or 
Bazin's  formulas  for  estimating  the  values  o<f  the  coefficient. 

Second — By  means  of  weirs  or  dams  of  such  form  that  the  coeffi- 
cient of  discharge  is  known,  and 

Third — By  the  measurement  of  the  cross  section  area  and  the 
velocity  of  current  passing  through  the  same. 

The  method  which  should  be  selected  for  any  particular  location 
depends  o<n  the  physical  conditions  of  the  problem,  the  degree  of 
accuracy  required,  the  expense  which  may  be  permissible  and  the 
length  of  time  during  which  the  record  is  to  be  continued. 

114.  Estimates  from  Cross-section  and  Slope. — Chezy's  formula, 


together  with  the  formulas  of  Kutter  and  Bazin,  for  the  determin- 
ation of  the  flow  of  streams,  has  already  been  discussed  in  Chapters 
III  and  X.  Much  information  is  now  available  in  regard  to  the 
value  of  the  coefficient  c,  but  this  value  varies  greatly  in  different 
streams,  in  accordance  with  the  conditions  of  the  beds,  and  in  the 
same  stream  under  various  conditions  of  flow.  The  results  obtained 
from  the  application  of  these  formulas  are  therefore  necessarily  very 
approximate.  The  method,  however,  is  of  considerable  value  in  es- 
timating the  flood  discharge  of  streams  and  in  obtaining  an  approxi- 
mate knowledge  of  flow  under  other  conditions  where  other  methods 
are  not  available  or  are  difficult  of  application. 

In  using  this  method  two  or  more  cross  sections  of  the  stream 
should  be  measured  on  reaches  of  the  river  where  the  cross  section 
and  other  conditions  are  fairly  uniform  and  can  be  readily  deter- 
mined and  at  a  time  when  the  flow  is  steady.  It  is  also  important 
that  the  stream  in  which  the  flow  is  to  be  estimated  shall  be  compar- 
able in  cross-section,  depth,  and  other  conditions,  on  which  the 
value  of  the  coefficient  c  depends,  with  other  streams  on  which  the 
value  of  c  has  been  determined. 

115.  Weir  Measurement. — Where  dams  are  so  located  that  they 
can  be  utilized  for  weir  measurements,  and  are  so  constructed  that 
such  measurements  are  reasonably  accurate,  or  where  suitable  weirs 
can  be  constructed  from  which  such  measurements  can  be  made, 
such  dams  and  weirs  afford  the  best  practicable  method  for  measure- 


22O  The  Measurement  of  Stream  Flow. 

ments  of  the  flow  of  a  stream.  In  order  to  assure  accurate  results  in 
weir  measurements,  the  following  conditions  must  be  fulfilled : 

First — The  dam  or  weir  must  have  sufficient  height  so  that  back 
water  will  not  interfere  with  the  free  fall  over  the  same ;  otherwise 
the  dam  will  be  available  for  purposes  of  measurement  only  during 
stages  when  no  such  interference  exists. 

Second — The  dam  or  weir  body  must  be  so  constructed  that  no 
leak  of  appreciable  size  will  occur  during  the  time  when  it  is  utilized 
for  measuring  purposes. 

Third — The  abutments  of  the  dam  or  sides  of  the  weir  must  be  so 
constructed  as  to  confine  the  flow  over  the  dam  at  all  stages :  other- 
wise the  weir  will  be  useless  for  measurements  during  flood  condi- 
tions. 

Fourth — the  crest  of  the  weir  must  be  level  and  must  be  kept  free 
from  obstructions  caused  by  floating  logs  or  ice. 

Fifth — The  crest  of  the  dam  or  weir  must  be  of  a  type  for  which 
coefficients  for  use  in  the  ordinary  weir  formula  have  been  deter- 
mined. (See  Chapter  III.) 

Sixth — If  the  dam  has  an  adjustable  crest,  great  care  must  be  used 
to  prevent  leakage  along  such  crest  and  to  keep  a  complete  and 
detailed  record  of  the  condition  of  the  crest  during  the  time  of  the 
observations. 

Seventh — If  water  is  diverted  around  the  dam,  which  is  usually 
the  case  when  a  dam  is  built  for  power  purposes  or  for  navigation, 
the  diverted  water  must  be  measured  or  estimated  and  added  to  the 
amount  passing  over  the  dam.  Such  diverted  water  can  sometimes 
be  measured  by  a  weir  or  current  meter.  When  such  water  is  used 
in  water  wheels,  an  accurate  record  of  the  gate  opening  of  the 
wheels  can  be  kept,  from  which  the  amount  of  water  used  in  the 
wheels  can  be  estimated  if  the  wheel's  discharge  has  been  calibrated 
or  if  the  wheel  is  of  some  well  known  type.*  The  conditions  for  the 
accurate  determination  of  weir  discharge  should  be  such  as  not  to 
involve  the  use  of  low  heads  of  less  than  6"  over  broad  crested  dams. 

Measurements  by  means  of  a  weir  or  dam  have  the  general  advan- 
tage of  continuity  of  record  during  the  periods  of  ice  and  flood  and 
the  disadvantage  of  uncertainty  of  the  coefficient  to  be  used  in  the 
weir  formula,  of  complication  by  the  diversion  of  water  around  the 
dam,  and  the  interference  of  flow  by  the  occasional  lodgement  of 
material,  or  of  injury  to  the  crest. 

*  See  Water  Supply  and  Irrigation  Paper  No.  180,— Turbine  Water  Wheel 
Tests  and  Power  Tables— by  R.  E.  Horton. 


The  Use  of  the  Current  Meter. 


221 


116.  Measurement  of  Flow  by  the  Determination  of  Velocity. — 

The  discharge  of  a  stream,  or  the  quantity  of  water  flowing  past  a 
certain  section  of  the  stream  in  a  given  time,  is  the  product  of  two 
factors :  first,  the  area  of  the  cross  section ;  and  second,  the  mean 
velocity  of  flow  through  said  section. 

If  the  flow  in  the  cross-section  of  the  stream  were  uniform  the 
measurement  erf  the  flow  would  be  a  simple  matter.  A  surface  float, 
timed  between  given  stations,  or  a  current  meter  placed  at  any 
point  in  the  cross-section,  would  then  indicate  the  average  velocity. 
Such  conditions,  however,  never  obtain.  It  is  therefore  necessary 
to  ascertain  the  mean  velocity  of  flow  in  the  section  which  is  a 
much  more  difficult  matter. 

Two  methods  of  measuring  the  velocity  of  a  stream  are  in  use: 
first,  by  the  use  of  a  current  meter,  and  second,  by  the  use  of 
floats.  Each  of  these  methods  has  advantages  peculiar  to  itself, 
which  must  be  knotwn  and  appreciated  in  order  that  intelligent 
measurements  may  be  made. 

117.  The  Use  of  the  Current  Meter. — The  current  meter   (Fig. 
119)  is  an  instrument  designed  to  revolve  freely  with  the  current  so 
that  by  determining  the  number  of  its  revolutions  the  velocity  of 


Fig.  119. — Price  Electric  Current  Meter  with  Buzzer. 


222 


The  Measurement  of  Stream  Flow, 

Section    A- A 


Fig.   120. — Cross   Section   of  small    Price   Electric   Current    Meter,    Showing 

details.* 

the  current  will  be  known.  A  well  made  current  meter  carefully 
maintained  and  frequently  rated  is  reasonably  accurate  when  prop- 
erly used  under  conditions  to  which  it  can  be  applied.  As  the  fric- 
tion of  operation  is  rarely  constant,  the  relation  of  current  velocities 
to  number  of  revolutions  is  not  always  strictly  proportional  and  it  is 
necessary  to  determine  the  relation  between  the  revolutions  of  the 
meter  and  the  corresponding  velocity  of  water.  This  is  accomplished 
by  rating  the  meter,  which  is  usually  done  by  passing  it  through 
still  water  at  known  velocities  and  noting  the  results.  It  is  assumed 
that  the  same  relation  will  exist  between  the  revolutions  of  the 
meter  and  its  longitudinal  velocity  through  still  water  and  between 
its  revolution  and  the  velocity  of  flowing  water' when  this  meter  is 
held  in  a  similar  position  in  a  stream.  The  meter  should  be  rated 
under  conditions  as  nearly  similar  as  possible  to  those  under  which 
it  was,  or  is  to  be,  used.  The  meter  when  being  rated  is  usually  at- 

*Prom  W.  S.  &  I.  Paper  No.  94  Hydrographic  Manual,  by  E.  C.  Murphy. 
J.  C.  Hoyt  and  G.  B.  Hollister. 


Current  Meter  Observations. 


223 


1LLL 


Fig.  121. — Current  Meter  Rating  Station  at  Denver,  Col.* 

tached  to  some  movable  device  (see  Fig.  121)  such  as  a  carriage  or 
boat  which  is  propelled  by  hand  or  machinery  at  a  known  rate  over 
a  fixed  distance.  Observations  of  the  revolutions  of  the  meter  at 
various  rates  of  speed  are  noted  and  the  relation  is  then  established 
between  the  velocity  of  the  meter  and  the  revolutions  of  the  meter 
wheel.  This  data  may  be  platted  upon  cross-section  paper  or  so 
arranged  in  tabular  form  that  the  corresponding  velocity  may  be 
immediately  ascertained  when  the  revolutions  of  the  meter  are 
known.  (See  Fig.  122.)  Experiments  have  shown  that  with  veloci- 
ties less  than  one-half  of  a  foot  per  second  little  or  no  dependence 
can  be  placed  upon  the  meter  observations  and  that  for  velocities 
below  one  foot  per  second,  the  meter  usually  under  registers.  Where 
such  low  velocities  obtain,  float  measurements  are  believed  to  be 
more  accurate. 

118.  Current  Meter  Observations  and  Computation. — On  account 
of  the  great  variation  in  velocity  at  different  points  in  the  cross-sec- 


*From  Hydrographic  Manual. 


224 


The  Measurement  of  Stream  Flow. 


7 

x 

x 

/ 

/ 

x 

/ 

x 

* 

Q2.8 

Sac 

X 

o 

UJ9     A 

/ 

<n2-4 

/ 

«2-2 

^90 

x 

Q.Z.O 

X" 

x 

<n  ••• 

Z 

X 

=  ,.. 

X 

_i 

0  1   9 

/ 

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£10 

t 

x 

X 

/ 

x^ 

x 

X1 

x 

4.0 

X 

3 

1 

- 

i 

i 

3 

1 

i, 

! 

VELOCITY.  IN    FEET    PER    SECOND 
Fig.  122.— Current  Meter  Rating  Curve. 

tion,  the  flow  through  any  unit  of  area  may  vary  more  or  less  from 
the  flow  through  other  similar  areas.  On  this  account  it  is  desir- 
able, in  order  to  systematically  survey  the  velocities  in  a  cross-sec- 
tion, as  well  as  for  ease  in  calculation,  to  divide  the  cross-section  area 
into  parts,  both  horizontally  and  vertically,  and  determine  the  actual 
velocity  of  each  of  said  parts.  As  a  basis  for  the  work,  the  cross- 
section  of  the  stream  should  first  be  obtained  by  sounding.  The 
vertical  sections,  chosen  for  the  purpose  of  water  observation,  are 
usually  five  feet  or  more  apart  but  the  horizontal  divisions  are 
usually  somewhat  less  as  the  variations  in  the  vertical  velocities  are 
usually  much  greater  than  in  horizontal  velocities.  The  size  of  both 
horizontal  and  vertical  division  depends  on  the  irregularity  of  the 
distribution  of  velocity  in  the  cross-section  as  well  as  on  the  ac- 
curacy required  in  the  determination  af  flow.  The  greater  the  care 
used  in  the  determination  of  the  velocities  in  the  unit  areas  and  the 
greater  the  number  of  such  sub-divisions  of  the  cross-section,  the 
more  accurate  will  be  the  work. 


UNIVERSITY 

CF 


Current  Meter  Computations.  225 

The  meter  readings  may  be  made  in  one  of  four  ways  : 

First—  By  determining  the  velocity  at  frequent,  definite  intervals 
of  depth  and  then  ascertaining  the  point  and  amount  of  average  velo- 
city in  each  vertical  section. 

Second  —  By  what  is  known  as  the  integration  method,  which 
consists  in  lowering  and  raising  the  meter  with  uniform  motion 
from  the  surface  to  the  bottom  of  the  vertical  section  and  noting  the 
average  velocity  determined  by  this  method. 

Third  —  By  making  a  point  measurement  at  the  depth  correspond- 
ing to  the  thread  of  mean  velocity  as  determined  in  the  first  method. 

Fourth  —  By  determining  the  velocity  at  some  other  point  of 
observation  and  deducting  the  mean  velocity  from  the  known  rela- 
tion of  the  point  measured  to  the  point  of  mean  velocity.  The  last 
two  methods  can  be  safely  used  where  the  vertical  velocity  curve 
lias  been  determined  with  sufficient  accuracy,  and  are  fairly  approxi- 
mate at  other  sections  where  the  conditions  are  not  of  an  unusual 
nature. 


Distance  from  inftial   point 
,/\5|0  I  610 


Fig.    123. — Cross-section   of   Saline   River   at   Guaging   Station   near    Salina, 

Kans. 

"Fig.  123  shows  the  cross  section  of  the  Saline  River  near  Salina, 
Kan.,  on  September  3<Dth,  1903,  while  the  discharge  measurements 
recorded  in  Table  XXII  were  being  made.  The  soundings  were 
taken  at  each  5  feet  of  width  from  the  initial  point  and  the  velocity 
was  observed  at  0.6  depths  below  the  surface  in  each  of  these  verti- 
cals. 

The  discharge  through  each  5-foot  strip  might  be  computed  sep- 
arately, but  the  computations  are  shortened  by  finding  the  discharge 
through  each  double  strip  at  a  time." 

*  From  Water  Supply  and  Irrigation  Paper  No.  94, — Hydrographic  Manual 
by  E.  C.  Murphy,  J.  C.  Hoyt  and  G.  B.  Hollister.  See  page  46  et  seq. 


226  The  Measurement  of  Stream  Flow. 

Let  d'm  =  mean  depth  for  double  strip; 
V'm  =  mean  velocity  for  double  strip; 
a,  b,  c  are  three  consecutive  depths,  L  feet  apart; 
Va  Vb  Vc    are  observed  velocities  in  the  verticals  a,  b,  c 
L  =  the  width  of  a  single  strip; 
Q'  =  the  discharge  through  double  strip. 

"The  mean  depth  and  the  mean  velocity  for  the  double  strip  of 
width  10  feet  are  found  from  the  formula  : 


C) 


The  discharge  through  the  double  strip  is . 
(3)        Q,=d.mV.m«L 


Formulas  (i)  and  (2)  are  based  on  the  assumption  that  the 
stream  bed  is  a  series  of  parabolic  arcs,  also  that  the  horizontal  ve- 
locity curves  are  parabolic  arcs,  both  of  which  assumptions  are 
approximately  true  at  good  current-meter  stations. 

In  computing  the  discharge  and  the  mean  depth  through  a 
single  strip  near  the  stream  bank  or  a  pier  the  mean  velocity  is 
found  from  the  formulas : 

(4)  Vm    =  ^°  +7a 


(5)  d  = 


where  either  Vo  or  Va  and  a'   or  a  may  be   "0". 

Velocity  is  computed  to  two  places  of  decimals,  mean  depth, 
area,  and  discharge  to  one  place  of  decimals  for  streams  of  ordinary 
size  ;  for  small  streams  with  hard,  smooth  botton,  where  depth  can 
be  measured  to  hundredths  foot,  the  mean  depth  and  area  should  be 
computed  to  two  places  of  decimals  and  the  discharge  to  one  place." 

These  observations  can  be  taken  in  shallow  streams  by  wading 
or  from  a  cable  car  (see  Fig.  124),  boat  or  bridge  as  the  circum- 
stances and  conditions  permit.  A  rope  or  cable,  marked  into  suit- 
able divisions  and  stretched  across  the  stream,  offers  the  best  means 
of  locating  the  horizontal  points  at  which  observations  in  the  verti- 
cal planes  are  to  be  made. 

119.  Float  Measurements.  —  Where  a  single  or  only  an  occasional 
measurement  of  the  flow  of  a  stream  is  to  be  made,  the  use  of  floats 


Current  Meter  Measurements. 


227 


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Salina,  State 

2.  Discharge,  1 


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Remarks.  (On  condition  of  chan- 
nel, wind,  equipment,  gage,  boat, 
cable,  methods,  accuracy.  Use 
cross-section  pages  in  back  of 
book  for  sketches.) 

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Velocity  computatoins. 

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t-t-OCrHlCOOCOt-t-^ 

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228 


The  Measurement  of  Stream  Flow. 


is  believed  to  be  preferable,  as  under  such  conditions  the  calibration 
of  the  current  meter  and  the  exercise  of  necessary  skill  in  its  use  are 
not  apt  to  receive  proper  attention.  Under  such  circumstances, 
therefore,  float  measurements  are  believed  to  be  more  accurate. 

In  the  use  of  floats  the  writer  usually  selects  round  soft  wood  one 
to  two  inches  in  diameter  and  in  various  lengths,  varying  by  about 
6".  These  are  weighted  at  the  lower  end,  usually  by  attaching  pieces 
of  lead  pipe  so  that  they  will  float  with  only  about  one  to  three 
inches  of  the  rod  exposed.  To  the  exposed  end  is  usually  attached 
small  red  or  white  streamers  so  that  they  may  be  readily  seen  and 
yet  not  be  seriously  affected  by  wind. 

A  point  for  the  gauging  is  selected  where  the  stream  is  fairly 
straight  and  uniform  in  section,  and  ropes,  wires,  or  cables  are 


Fig.  124.— Cable  Station,  Car  Guage,  etc. 

stretched  tightly  across  the  stream,  parallel  to  each  other  and  25,  50 
or  100  feet  apart,  as  the  location  and  velocity  of  the  stream  seem 
to  demand.  The  ropes  or  wires  should  be  tagged  at  intervals  of  5, 
10  or  25  feet,  as  the  conditions  seem  to  warrant,  beginning  at  zero  on 
the  straight  bank. 

In  starting  the  work  a  float  is  selected  that  will  reach  as  near  the 
bottom  as  possible  without  touching  and  should  be  about  .9  depth. 
The  float  is  started  5  to  10  feet  above  the  upper  line  and  so  placed 
that  it  will  pass  as  nearly  as  possible  under  one  of  the  tags.  The 
point  at  which  it  actually  passes  under  the  line  is  noted  and  re- 
corded, also  the  point  and  time  at  which  it  passes  the  lower  line.  If 
the  float  should  touch  the  bottom  or  a  snag  in  its  passage,  the  next 
shorter  length  should  be  used  until  the  float  passes  both  lines  freely. 
Floats  should  be  run  at  frequent  intervals  across  the  stream  usually 
at  each  of  the  tagged  stations. 


The  Application  of  Stream  Gaugings.  229 

Extensive  experiments  were  made  by  Francis  at  Lowell,  Mass., 
in  1852  to  determine  the  accuracy  of  rod  float  measurements.* 

He  found  that  discharge  measurements  based  on  the  determina- 
tion of  velocities  by  floats  were  nearly  always  large  as  compared 
with  measurements  by  a  standard  weir.  This  was  due  to  the  fact 
that  the  rod,  on  account  of  not  reaching  the  bottom,  was  not 
affected  by  the  low  velocity  near  the  stream  bed  and  hence  indi- 
cated too  great  a  velocity.  He  found  that  the  effect  could  be  cor- 
rected by  multiplying  the  discharge  as  obtained  by  the  floats  by  a 
coefficient  as  follows : 

(6)  Q  =  CQA  in  which 

Q  =  actual  discharge 

Q!  =  discharge  as  determined  by  floats. 

C  =  coefficient  =  1—0.116  (l/lT—  0.1)  and 

..    distance  of  bottom  of  float  from  bottom   of  stream 

D    •=•  ratio j : j 

depth  of  stream. 

It  will  be  observed  that  this  coefficient  C  is  always  less  than 
unity  except  where  D  is  less  than  o.oi  which  condition  could  not 
be  possible  in  any  natural  stream. 

The  Francis  experiments  were  made  in  a  channel  of  rectangular 
cross  section  and  floats  of  uniform  length  were  used.  In  a  natural 
stream  the  depth  will  vary  at  different  points  in  the  cross  section 
and  floats  of  different  lengths  must  be  used.  In  such  cases  D  will 
vary  widely  for  the  various  floats  used  and  to  apply  the  correction, 
the  velocity  as  determined  by  each  float  should  be  reduced  by  its 
particular  consatnt,  C. 

Experiments  made  at  the  Cornell  Hydraulic  Laboratory  in  1900 
by  Kuichling,  Williams,  Murphy  and  Boright  confirmed  Francis' 
conclusion  that  rod  float  measurements  are  too  large,  only  two  out 
of  thirty  being  smaller  than  measurements  made  by  a  standard 
weir.  No  attempt  was  made,  however,  to  verify  Francis'  formula 
for  the  correction  of  such  observations.* 

In  calculating  the  discharge  from  these  measurements  the  ave- 
rage cross-section,  in  cubic  feet,  of  each  division  is  calculated  and 
multiplied  by  the  average  velocity  for  the  same  in  feet  per  second 
and  the  product  will  represent  the  discharge  in  cubic  feet  per  second 
of  the  section  represented  by  that  float  and  the  sum  of  the  sections 
of  all  the  floats  will  give  the  total  discharge  of  the  stream. 

*  See  "Lowell  Hydraulic  Experiments"  by  James  B.  Francis,  pp.  146-208. 

*  See  W.  S.  &  I.  Paper  No.  95,  Accuracy  of  Stream  Measurements,  p.  54. 


230 


The  Measurement  of  Stream  Flow. 


10    20    30    40    50    60    70    80    90    100   110 


Fig.  125.— Graphic  Determination  of  Stream  Flow  From  Measurements. 


The  Application!  of  Stream  Gaugings.  231 

It  is  frequently  desirable  to  calculate  the  discharge  graphically, 
which  may  be  done  as  shown  by  Fig.  125.  This  is  done  by  plotting 
the  two  sections  at  the  tag  lines  over  each  other  and  drawing  in  an 
average  section  between  them.  It  is  frequently  desirable  to  draw 
in  the  floats  in  their  true  length  and  average  position  so  that  it  may 
be  seen  at  once  how  well  the  section  was  covered  by  the  floats. 

Under  each  float  is  laid  off  the  velocity  as  determined  by  the 
same,  to  a  selected  scale,  and  a  mean  velocity  curve  is  drawn 
through  these  points.  By  multiplying  the  ordinate  of  the  velocity 
curve  by  the  ordinates!  of  the  mean  section,  a  quantity  is  obtained 
on  the  discharge  curve  which,  when  fully  constructed,  gives  a  dis- 
charge polygon,  the  area  of  which  represents  at  the  correct  scale 
the  discharge  in  cubic  feet  per  second  of  the  stream. 

1 20.  The  Application  of  Stream  Gaugings. — A  single  measure- 
ment of  stream  flow  is  of  comparatively  little  value  as  a  basis  for  es- 
timating the  continuous  character  of  the  flow  of  the  stream,  as  will 
be  seen  by  examination  of  any  of  the  hydrographs  previously  shown. 
The  flow  of  a  stream,  while  it  may  appear  to  the  casual  observer  uni- 
form, is  actually  subject  to  many  and  violent  fluctuations  and  the 
flow  may  vary  several  hundred  per  cent,  from  minimum  to  maxi- 
mum within  a  few  days. 

It  has  already  been  pointed  out  that  in  order  to  study  the  flow  of  a 
stream  intelligently  it  is  necessary  to  know  the  variations  in  flow 
that  take  place  from  day  to  day  for  a  long  term  of  years  during 
which  the  effect  of  the  extreme  of  all  of  the  factors  controlling 
•stream  flow  may  have  made  themselves  manifest. 

The  actual  measurement  of  the  flow  of  a  stream  by  current  meter 
•or  floats  is  usually  accomplished  with  considerable  difficulty,  and  it 
would  be  practically  impossible  to  repeat  such  measurements  daily 
for  the  length  of  time  for  which  records  are  desired.  It  has 
already  been  pointed  out  that  under  many  conditions  it  is  possible 
to  establish  a  discharge  or  rating  curve  which  will  show  the  relation 
of  the  height  of  the  water  surface  to  the  flow  through  orifices  over 
weirs  or  through  channels  of  various  forms.  In  the  establishment  of 
such  relation  it  is  assumed  that  the  raising  of  the  water  surface  to  a 
given  height  is  always  accompanied  by  the  same  flow  of  water 
through  the  section.  In  order  to  assure  accuracy  in  the  observa- 
tions based  on  such  a  rating  curve,  sections  must  be  selected  where 
the  conditions  assumed  are  correct.  Such  stations  should  be  se- 
lected, where  possible,  on  a  fairly  long  uniform  reach  of  the  stream 


232 


The  Measurement  of  Stream  Flow. 


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0  10.000  20,000  30,000  40,000  50.000  60.000  70,000  80.000  90.000  100.000  110 
Discharge  in  second-feet 

Fig,  126,  —  Discharge,  Velocity  and  Area  Curved  for  the  Potomac  River  at  Poin 

, 

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MEASUREMENTS  IN  /9O^  NO.  1 
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Literature.  233 

and  beyond  the  influences  of  the  back  water  from  large  rivers  or 
dams. 

After  gaugings  of  the  stream  have  been  made  under  a  considerable 
range  of  conditions  and  a  rating  curve  is  established  therefrom,  it  is 
not  necessary  thereafter  to  measure  the  daily  flow  but  only  to  note 
daily  the  gauge  height.  It  has  been  determined  by  many  observa- 
tions that  under  constant  conditions  a  fixed  relationship  exists  be- 
tween gauge  height  and  the  discharge  of  a  stream,  subj-ect  to  the 
errors  due  to  variable  flow  as  described  in  Chapter  X.  If  the  section 
and  other  conditions  of  the  stream  flow  remain  unchanged,  the  rat- 
ing curve  will  remain  constant  and  hence  the  daily  gauge  height 
can  be  quickly  read  and  recorded  and  will  give  at  once,  by  reference 
to  the  rating  curve  or  table,  the  quantity  of  water  flowing  in  the 
stream  at  all  times. 

From  the  soundings  and  levels  made  to  determine  the  cross  sec- 
tion, an  area  curve  can  be  constructed  showing  the  variation  of 
area  with  gauge  height.  The  float  or  current  meter  observations 
furnish  the  necessary  data  for  the  construction  of  a  curve  of  mean 
velocities.  The  product  of  the  area  and  mean  velocity,  as  shown 
by  these  two  curves,  for  any  given  gauge  height,  must  equal  the 
discharge  and  must  equal  the  reading  of  the  discharge  curve  for 
the  same  gauge  height.  The  construction  of  these  curves,  and  a 
consideration  of  their  properties,  furnishes  a  check  on  the  construc- 
tion of  the  discharge  curve  and  aids  materially  in  correcting  any 
apparent  irregularities  therein.* 

Fig.  126  shows  the  discharge,  mean  velocity  and  area  curves  for 
the  Potomac  River  at  Point  of  Rocks,  Aid. 


LITERATURE. 

STREAM   GAUGING. 

1.  Baumgarten,  M.     Pulsations  of  Velocity  in  River  Current.     Annales  des 

Fonts  et  Chaussees.    1847. 

2.  A  Study  of  the  Law  of  Flows  in  Rivers,  Oscillations  of  Velocity,  Obser- 

vations of  Vertical   and  Transverse  Velocity  Curves.     Annales 
des  Fonts  et  Chaussees.    1847. 

3.  Croes,   Jas.  R.     Flow  of  the  West  Branch  of  the  Croton   River,  N.  Y. 

Trans.  Am.  Soc.  C.  E.  vol  3,  pp.  76-90.     1874. 

4.  Ellis,  Theo.  G.     Flow  of  Water  in  Open  Channels.     Trans.  Am.  Soc.  C.  E. 

vol.  6,  pp.  250-258.  1877. 


*See  "River  Discharge," — Hoyt  and  Grover. 
14 


234  The  Measurement  of  Stream  Flow. 

5.  Wood,  de  Volsen.    Flow  of  Water  in  Rivers.     Trans.  Am.  Soc.  C.  E.  vol. 

8,  p.  173.    1879. 

6.  McMath,  R.  E.    River  Hydraulics.     Trans.  Am.  Soc.  C.  E.  vol.  9,  pp.  378- 

390.    1880. 

7.  McMath,  R.  E.    The  Mean  Velocity  of  Streams  Flowing  in  Natural  Chan- 

nels.   Trans.  Am.  Soc.  C.  E.  vol.  11,  pp.  186-211.    1882. 

8.  Current  Meter  Measurements  on  the  Rhine.    Allgemeine  Bauzeitung,  Vol. 

47,  pp.  53-80.     1882. 

9.  Unwin,  W.  C.     Current  Meter  Observations  in  the  Thames.     Proc.  Inst. 

C.  E.     Vol.  71,  p.  338.     1883. 

10.  Stearns,  F.  P.    Why  the  Maximum  Velocity  is  Below  the  Surface.    Trans. 

Am.  Soc.  C.  E.    Vol  12,  p.  331.  1883. 

11.  Cunningham,  Allan.     Recent  Hydraulic  Experiments.     Proc.   Inst.  C.  E. 

Vol.  71,  p.  1.    1883. 

12.  Fteley,  A.  and  Stearns,  E.  P.     Description  of  Some  Experiments  on  the 

Flow  of  Water.    Trans.    Am.  Soc.  C.  E.    Vol.  12,  pp.  1-118.     1883. 

13.  Measurement  of  Water.    Bui.  G,  Montana  Agric.  Expt.  Sta.     1885. 

14.  Isakoski,  R.     Discharge  of  Rivers  from  the  Drainage  Areas.     Zeitschr. 

d  Oesterr.  Ing.  u  Arch.  Ver.     1886,  pp.  69-98. 

15.  Seddon,  J.  A.     Consideration  of  the  Relation  of  Bed  to  the  Variables. 

Jour.  Assn.  Eng.  Soc.    Vol  5,  p  .  127.     1886. 

16.  The  Determination  of  Normal  Cross-Sections  of  the  Elbe.    Taubert.    Zeit- 

schrift  fur  Bauwesen,  pp.  551-562.     1886. 

17.  Green,  J.  S.    Fourth  Biennial  Report  State  Eng.  of  Colo.     1889. 

18.  Bazin,  M.     Recent  Experiments  on  the  Flow  of  Waters  over  Weirs.     An- 

nales  des  Fonts  et  Chaussees,  Oct.  1888;  see  also  Proc.  Eng.  Club 
of  Phila.    Vol  7  p  260.    1890. 

19.  Flynn,  P.  J.     Flow  of  Water  in  Irrigation  Canals.     San  Francisco.     Pub- 

lished by  the  Author.    1892. 

20.  Ganguillet,  E.  and  Kutter,'  W.  R.     A  General  Formula  for  the  Uniform 

Flow  of  Water  in  Rivers  and  Other  Channels.    Trans,  by  Hering 
and  Trautwine.    New  York.    Wiley  &  Sons.    1893. 

21.  Foss,  W.  E.    New  Formula  for  Calculating  the  Flow  of  Water  in  Pipes  and 

Channels.    Jour.  Asso.  Eng.  Soc.    Vol.  13,  p.  295.    1894. 

22.  Flynn  and  Dyer.    The  Cippoletti  Trapezoidal  Weir.    Trans.  Am.  Soc.  C.  E. 

Vol.  32,  p.  9,  1894. 

23.  Carpenter,  L.  G.     Measurement  and  Division  of  Water.     Bui.   27,  Colo. 

Agric.  Expt.  Sta.,  Fort  Collins,  Colo.     1894. 

24.  Newell,  F.  H.     Discharge  Measurements  of  Streams.     Proc.  Eng.  Club, 

Phila.    Vol.  12,  No.  2,  p.  125.     1895. 

25.  Humphreys,  D.  C.    Discharge  Measurements.    Jour.  Assn.  Eng.  Socs.    Vol. 

15,  No.  5,  p.  187.    1895. 

26.  Starling,  Wm.     The  Discharge  of  the  Mississippi.  Trans.  Am.  Soc.  C.  E. 

Nov.  1895. 

27.  Grunsky,  C.  E.     Method  for  Approximate  Gauging  of  Rivers.     Eng.  Rec. 

March  7,  1896 

28.  Keating,  W.  J.    Coefficients  in  Hydraulic  Formulas.    Jour.  Wes.  Soc.  Eng. 

Vol.  1,  p.  190.    1896. 

29.  Johnson,  F.  T.  and  Cooley,  E.  L.    Experimental  Data  for  Flow  over  Broad 

Crest  Dam.  Jour.  Wes.  Soc.  Eng.    Vol.  1,  p.  30.    1896. 


Literature. 


235 


30.  A  Study  of  Gauging  Statistics.    Annales  des  Fonts  et  Chaussees.    Part  III. 

1897. 

31.  Jasmund,  R.     Variation  in  Velocity  in  Cross-  Section  of  a  Stream,  Es- 

pecially with  Obstructions  on  the  Surface  and  Ice.  Zeitschr.  fur 
Bauwesen.  1897,  pp.  303,  465,  585.  Centrallb.  der  Bauverwaltung 
p.  101. 

32.  Johnson,  Clarence  T.     Stream  Gaugings.     Proc.  Purdue  Soc.  Civ.  Eng. 

1897. 

33.  Skinner,  John  W.     Description  of  the  Method  of  Gauging  the  Discharge 

Through  the  Outlet  of  Hemlock  Lake,  N.  Y.  Trans.  Assn.  Civ. 
Engs.  of  Cornell  University.  1898. 

34.  Bindemann,  H.    Difference  Between  Average  Flow  and  Flow  at  Center  of 

Stream.     Centralblatt  der  Bauverwaltung,  p.  638.     1898. 

35.  Lippincott,  J.  B.    Low  Water  Measurements  in  the  State  of  California  dur- 

ing the  Summer  of  1898.    Eng.  News.    Jan.  12,  1899. 

36.  Average  Velocity  of  Water  in  Natural  Streams.     Zeitschrift.  fur  Gewas- 

ser,  pp.  20-36.    1899. 

37.  Newell,  F.  H.     Stream  Measuring  in  the  United  States.     Sci.  Am.  Sup. 

Nov.  11,  1899. 

38.  Fuchs,  Paul.     The  Measurement  of  the  Velocity  of  Flow  of  Streams.    Ge- 

sundheits  Ing.     Nov.  30,  1899. 

39.  Stewart,  Clinton  B.     Discharge  Measurements  of  the  Niagara  River  at 

Buffalo,  N.  Y.     Jour.  W.  Soc.  Engs.     Dec.  1899. 

40.  Investigation  of  Relationship  of  Average  Flow  of  a  Stream  with  the  Flow 

at  the  Center.    Zeitschrift  fur  Gewasser,  p.  212.    1900. 

41.  Manner  of  Movement  of  water  in  Streams.    Zeitschr.  fur  Bauwesen.    Nos. 

VII  to  IX.    Centralblatt  der  Bauverwaltung,  p.  611.    1900. 

42.  Methods  of  Stream  Measurement.     Water  Supply  and  Irrigation  Paper 

No.  56.     1901. 

43.  Murphy,  E.  C.    Accuracy  of  Stream  Measurement.    Water  Supply  and  Irri- 

gation Paper,  No.  64.     1901. 

44.  Turneaure  and  Russell.     Public  Water  Supplies.     Chap.  12.     New  York. 

Wiley  &  Sons.     1901. 

45.  Tutton,  C.  H.     The  Laws  of  River  Flow.     Jour.  Assn.  Eng.  Socs.     Jan. 

ary,  1902. 

46.  The  Natural  Normal  Sections  of  Streams.  Zeitschr.  d  Oesterr.  Ing.  u  Arch 

Ver.    Feb.  21,  1902. 

47.  Relation  of  Surface  to  Mean  Velocities  of  Flow.— An  Investigation  Con- 

ducted by  J.  B.  Lippincott  and  others  in  the  West.  Eng.  News. 
Vol.  1,  p.  424.  1902. 

48.  Annual  Report  Chief  Eng.  U.  S.  A.    1900.    Appendix  I.  I.  I.    Survey  of  N. 

and  N.  W.  Lakes.  Same  1902.  Appendix  E.  E.  E.  and  1903  Ap- 
pendix F.  F.  F. 

49.  Pressey,  H.  A.  Methods  of  Measuring  Velocity  in  River  Channels.    Sci.  Am. 

Sup.     Sept.  5,  1903. 

50.  Merriman,  Mansfield.    Treatise  on  Hydraulics.    New  York.    Wiley  &  Sons. 

1903. 

51.  Bellasis,  E.  D.     Hydraulics  with  Tables.     New  York.     D.  Van  Nostrand 

Company.     1903. 


236  The  Measurement  of  Stream  Flow. 

52.  Murphy,  E.  C.,  Hoyt,  J.  C.  and  Hollister,  G.  B.     Hydrographic  Manual  of 

the  U.  S.  G.  S.    Water  Supply  &  Irrigation  Paper  No.  94.     1904. 

53.  Hoyt,  John  C.     Methods  of  Measuring  the  Flow  of  Streams.     Eng.  News. 

Jan.  14,  1904. 

54.  Miller,  C.  H.,  Pratt,  R.  W.,  Robinson,   H.   F.     Methods  of  Determining 

the  Mean  Velocity  of  Cross-Sections.     Eng.  News.     Vol.   1,  pp. 
258-307.    1904. 

55.  Anderson,  R.  H.     Some  Flood  Discharges  and  Values  of  "n"  in  Kutter's 

Formula.    Eng.  News.    Aug.  4,  1904. 

56.  Hoyt,  John  C.    Methods  of  Estimating  Stream  Flow.    Eng.  News.    Aug.  4, 

1904. 

57.  Recent  Russian  Studies  of  Flow  in  Rivers.    Eng.  News.     Sept.  1,  1904. 

58.  Stout,  O.  V.  P.     Notes  on  Computation  of  Stream  Measurements.     Eng. 

News.     Vol.  2,  pp.  521-547.     1904. 

59.  Mullins,  J.,  and  Span,  F.  N.     Irrigation  Manual.  1905. 

60.  Hermanek,  Johann.     The  Mean  Velocity  in  Natural  and  Artificial  Chan- 

nels.   Zeitschr.  d  Oesterr.  Ing.  u  Arch  Ver.    Apr.  21,  1905. 

61.  Murphy,  E.  C.    A  Method  of  Computing  Flood  Discharge  and  Cross-Section 

Area  of  Streams.     Eng.  News.     Apr.  6,  1905. 

62.  Barrows,  H.  K.    Work  of  the  Hydrographic  Branch  of  the  United  States 

Geol.  Sur.  in  N.  E.  and  a  Discussion  of  the  Methods  used  for  Es- 
timating Stream  Flow.     Jour.  Assn.  Eng.  Socs.     July,  1905. 

63.  Butcher,  W.  L.    The  Gaging  of  Streams  by  Chemical  Means.    Eng.  News. 

Dec.  14,  1905. 

64.  Hoyt,  J.  C.  and  Grover,  N.  C.    River  Discharge.    New  York.     J.  Wiley  & 

Sons.    1907. 


CHAPTER  XII. 

WATER  WHEELS. 

121.  Classification   of    Water   Wheels. — Water    wheels    include 
most  of  the  important  hydraulic  motors  that  are  adaptable  to  large 
hydraulic  developments.     They  may  be  divided  into  three  classes, 
viz: 

First — Gravity  wheels. 

Second — Reaction  wheels. 

Third — Impulse  wheels. 

In  gravity  wheels  the  energy  of  the  water  is  exerted  by  its  weight 
acting  through  a  distance  equal  to  the  head. 

In  both  reaction  and  impulse  wheels  the  potential  energy 'due  to 
the  weight  of  the  water  under  the  available  head  is  first  converted 
into  kinetic  energy.  This  kinetic  energy  does  work  in  the  reaction 
wheel  through  the  reactive  pressure  of  the  issuing  streams  upon 
the  movable  buckets  from  which  they  issue. 

In  the  impulse  wheel  the  nozzles  or  guides  are  stationary  and 
the  energy  of  the  issuing  streams  is  utilized  by  the  impulsive  force 
which  they  exert  in  impinging  against  movable  surfaces  or  buckets. 

Figs.  127,  128  and  129,  which  illustrate  the  various  types  of 
wheels  included  in  the  above  classes,  are  adapted,  with  many  mod- 
ifications from  Reuleaux's  "Constructor."  : 

122.  Gravity  Wheels. — Fig.  127  shows  the  various  types  of  grav- 
ity water  wheels  or  those  wheels  that  are  driven  by  the  weight  of 
the   water.      At   moderate   velocity,   these   motors    are    practically 
operated  by  gravity  only,  although  under  some  conditions  the  im- 
pulse due  to  the  velocity  of  the  entering  water  may  have  an  appreci- 
able effect.     In  Fig.   127,  A  is  an  undershot  water  wheel ;  B  is  a 
half-breast  wheel  (see  also  Figs.  3  and  4),  and  C  is  a  high  breast 
wheel.    D  is  an  overshot  wheel.    In  C  and  D  the  buckets  should  be 
so  designed  as  to  retain  the  water  until  they  reach  the  lowest  point 
in  the  revolution  of  the  wheel.     E  in  this  Figure  illustrates  Dup- 


*  "The  Constructor."     F.  Reuleaux — trans,  by  H.  H.  Suplee,  Philadelphia. 
Pa.,  1893. 


238 


Water  Wheels. 


A 


D 


ii  I  J 

Fig.  127. — Diagram  of  Gravity  Wheels. 


Reaction  Wheels. 


239 


pinger's  side-fed  wheel.  F  illustrates  an  endless  chain  of  buckets 
which  is  essentially  the  same  in  principle  as  the  overshot  wheel.  G 
is  a  similar  arrangement  using  discs  running  with  as  small  a  clear- 
ance as  possible  in  a  vertical  tube.  When  the  water  acts  only  by 
gravity,  the  wheels  represented  by  A  to  E,  inclusive,  are  only  prac- 
ticable when  the  wheel  can  be  made  as  large  or  larger  in  diameter 
than  the  fall  of  the  water.  Where  small  diameters  must  be  used, 
the  arrangements  shown  in  F  and  G  are  available.  Very  small 
wheels  acting  under  high  pressures  may  be  employed  by  making 
use  of  the  so-called  chamber  wheels,  illustrated  in  H,  I  and  J. 

123.  Reaction  Wheels. — The  wheels  illustrated  by  the  diagrams 
in  Fig.  128  are  of  the  second  class  or  reaction  wheels.  Diagram  A 
illustrates  Barker's  Mill  of  the  form  known  as  the  Scotch  turbine 
illustrated  also  by  Fig.  8.  This  form  of  turbine  is  known  in  Ger- 
many as  the  Segner  wheel.  The  water  enters  the  vertical  axis  and 
discharges  through  the  curve  arms.  B  represents  a  screw  turbine 
which  is  entirely  rilled  with  water.  C  shows  a  Girard  current  tur- 
bine which  has  a  horizontal  axis  and  is  only  partially  submerged. 
D  is  Cadiat's  turbine  with  central  delivery.  It  resembles  the  Four- 
neyron  turbine  except  that  there  are  no  guides  to  direct  the  flow 
into  the  buckets.  E  is  Thompson's  turbine  with  circumferential 
delivery  and  horizontal  axis.  The  discharge  from  this  turbine  is 
about  the  axis  at  both  sides. 

In  diagrams  A,  B,  C,  D  and  E  the  column  of  water  is  received  as  a 
whole  and  enters  the  wheel  undivided.  The  remainder  of  the  forms 
illustrated  in  Fig.  128  show  wheels  in  which  the  flow  is  divided  into 
a  number  of  separate  streams  by  guides  interposed  in  the  streams 
before  the  water  enters  the  wheel.  Diagram  F  illustrates  the  Four- 
neyron jturbine  which  acts  with  central  delivery.  The  guide  veins 
arTfixed  and  the  discharge  of  the  water  is  at  the  circumference  of 
the  wheel.  The  ordinary  vertical  form  of  the  Fourneyron  turbine  is 
illustrated  in  Fig.  128.  Diagram  G,  also  in  Fig.  128,  is  a  modification 
of  the  Fourneyron  turbine  in  which  the  water  is  being  delivered 
upward  from  below.  This  form  is  sometimes  called  the  Nagel's  tur- 
bine. Diagram  H  is  the  Jonval  or  Henschel  turbine.  (See  also 
Fig-  I35-)  The-  guide  vanes  in  this  turbine  are  above  the  wheel 
which  is  entirely  filled  by  the  water  column.  Diagram  J  is  the 
Francis  turbine  in  practically  its  original  form.  (See  also  Fig.  14.) 
Diagram  I  illustrates  the  present  American  form  or  modification  of 
the  original  Francis  turbine.  K  is  the  Schiele  turbine,  a  double 
wheel  with  circumferential  delivery  and  axially  directed  discharge. 


240 


Water  Wheels. 


I 


Fig.  128. — Diagrams  of  Reaction  Wheels 


Impulse  Wheels.  241 

In  forms  H,  I,  J  and  K,  a  draft  tube  may  be  used  below  the  wheel  to 
utilize  any  portion  of  the  fall  which  occurs  below  the  level  of  the 
bottom  of  the  wheel. 

In  all  reaction  turbines,  the  water  acts  simultaneously  through  a 
number  of  passages  around  the  entire  cirpumference  of  the  wheel. 
In  the  impulse  or  action  turbine,  the  water  may  be  applied  to  all  of 
the  buckets  simultaneously  or  to  only  a  portion  of  the  circumference 
at  a  time. 

124.  Impulse  Wheels. — The  wheels  illustrated  in  Fig.  129  are  the 
third  class  of  wheels  which  are  driven  by  the  impulse  due  to  the 
weight  of  water  acting  through  its  velor.ity.    Of  these  wheels,  A  is 
the   current   wheel   or   common   paddle   wheel.     The   paddles   are 
straight  and  either  radial  or  slightly  inclined  toward  the  current, 
as  in  the  illustration.     (See  also  Figs.  I  and  2.) 

Diagram  B  is  Poncelet's  wheel.  (See  also  Fig.  5.)  The  buckets 
run  in  a  grooved  channel  and  are  so  curved  that  the  water  drives 
upward  and  then  falls  downward,  thus  giving  a  better  contact. 

Diagram  C  shows  an  externally  driven  tangent  wheel.  The  buck- 
ets are  similar  tx>  the  Poncelet  wheel  but  with  a  sharper  curve 
inward.  The  discharge  of  the  water  is  inward.  D  is  an  internally 
driven  tangent  wheel  similar  to  the  preceding  but  with  an  outward 
discharge. 

E  is  the  so-called  hurdy-gurdy  or  tangential  wheel.  The  water 
is  delivered  through  a  nozzle  and  the  wheel  is  practically  an  ex- 
ternally driven  tangent  wheel  of  larger  diameter  and  with  a  smaller 
number  of  buckets. 

Diagrams  F,  G  and  H  illustrate  three  types  of  impulse  wheels 
with  inclined  delivery.  (See  also  Figs.  6,  7,  9  and  10.)  Diagram  F 
shows  a  crude  form  of  vertical  wheel  similar  in  form  to  the  Indian 
wheel,  Fig.  6.  It  is  used  on  rapid  mountain  streams  and  is  probably 
the  original  conception  from  which  the  turbine  has  been  developed. 
Diagram  G  is  the  Borda  turbine  and  consists  of  a  series  of  spiral 
buckets  in  a  barrel-shaped  vessel.  Diagram  H  is  a  Danaide  turbine 
which  has  spiral  buckets  enclosed  in  a  conical  tube.  This  is  an  old 
form  of  wheel  formerly  used  in  France. 

125.  Use  of  Water  Wheels.— Almost  all  water  wheels  in  prac- 
tical use  are  modifications  of  some  of  the  above  forms  and  by  a 
study  of  these  forms  a  wheel  may  be  classified  and  a  clearer  under- 
standing obtained  of  the  principles  of  its  operation.     Many  of  the 
forms  of  wheels  shown  in  Figs.  127,  128  and  129  are  practically  ob- 
solete or  are  used  onlv  in  minor  plants  or  for  special  conditions 


242 


Water  Wheels. 


B 


H 


Fig.  129. — Diagrams  of  Impulse  Wheels 


Use  of  Water  Wheels.  243 

that  make   them   of   only  general   interest  in  the   study  of   water 
power. 

While  gravity  wheels  are  still  occasionally  used  their  application 
is  entirely  to  the  smaller  water  power  plants.  In  many  cases  the 
turbines  purchased  for  such  installations  are  of  cheaper  make, 
poorly  designed,  constructed  and  selected,  and  often  improperly  set 
and,  consequently,  inefficient.  In  such  cases,  and  where  the  ques- 
tion of  back  water  and  the  interference  of  ice  is  not  important,  the 


Fig.  130.— "Overshot"  Water  Wheel.     Manufactured  by  Fitz  Water  Wheel  Co. 

gravity  wheel  may  be  more  efficient  and  quite  satisfactory.  Well 
designed  and  well  constructed  gravity  wheels  are  said  to  give  effi- 
ciencies of  85  per  cent,  and  above.  (See  Frontispiece  and  Fig. 
130).  With  such  plants  the  engineer  has  usually  little  to  do  and 
consequently  they  will  not  be  further  considered  here.  The  types 
of  wheels  now  most  largely  used  for  moderate  and  large  water 
power  developments  are  the  reaction  and  impulse  turbines. 

126.  Classification  of  Turbines.— All  moder  turbines  consist  of 
a  wheel  to  which  buckets  are  attached  and  whicn  is  arranged  to  re- 
volved in  a  fixed  case  having  attached  to  it  a  nozzle,  guide  or 


244  Water  Wheels. 

series  of  guides.  The  guide  passages  or  nozzles  direct  the  water 
at  a  suitable  angle  onto  the  buckets  of  the  wheel.  The  revolving 
wheel  contains  curved  buckets  or  passages  whose  functions  are  to 
receive  the  water,  utilize  its  energy  and  discharge  or  waste  it  as 
nearly  devoid  of  energy  as  possible. 

Turbines  may  be  classified  in  various  ways: 

First. — In  accordance  with  the  action  of  the  water  on  the  same. 

(A)  Reaction  or  pressure  turbines,  such  as  the  Fourneyron,  Jon- 
val,  Francis,  etc.     (See  Fig.  128,  G,  H,  I  and  J.) 

(B)  Action  or  impulse  turbines,  such  as  the  Girard  and  tangen- 
tial wheels.     (See  Fig.  129,  diagrams  D  and  E.) 

(C)  Limit  turbines,  which  may  act  either  by  reaction  or  impulse. 
Second. — In  accordance  with  the  direction  of  flow  in  reference 

to  the  wheel. 

(A)  Radial   flow   turbines.     In   these    turbines    the   water   flows 
through  the  wheel  in  a  radial  direction.     These  may  be  subdivided 
into — 

(a)  Outward  radial  flozv  turbines,  such  as  the  Fourneyron  and 
Cadiat.     ,(See  Fig.  128,  diagrams  F  and  D.) 

(b)  Inward  radial  flow  turbines,  or  wheels  in  which  the  water 
flows  inward  in  a  radial  direction  such  as  the  Francis  and  Scheile 
turbines.     (See  Fig.  128,  J  and  K.) 

(B)  A. vial  flow  turbines  in   which   the  general   direction   of  the 
water  is  parallel  to  the  axis  of  the  wheel  such  as  the  Jonval  and 
Girard  wheels  of  similar  design.     (See  Fig.  128,  H.) 

(G)  Mixed  flow  turbines,  or  turbines  in  which  the  flow  is  par- 
tially radial  and  partially  axial  as  in  turbines  of  the  American  type. 
(See  Fig.  128,  diagram  I;  also  Figs.  143  to  158  inclusive). 

Third. — In  accordance  with  the  position  of  the  wheel  shaft. 

(A)  Vertical  (See  Figs.  132,  134,  135,  151,  etc.). 

(B)  Horizontal  (See  Figs.  140,  152.) 

Fourth. — In  accordance  with  the  arrangement  of  nozzles  or 
guides. 

(A)  Complete  turbines  with  guides  surrounding  the  entire  wheel. 

(B)  Partial  turbines  with  guides  partially  surrounding  the  wheel 
in  one  or  more  groups. 

The  re-action  turbine  is  a  turbine  with  restricted  discharge  which 
acts  through  the  reactive  pressure  of  the  water.  Under  some  con- 
ditions the  energy  of  the  water  may  be  exerted,  at  least  in  part, 
by  its  impact  or  momentum.  The  impulse  turbine  acts  princip- 


Condition  of  Operation.  245 

ally  through  the  momentum  of  the  moving  mass  of  water  although, 
when  the  current  reverses,  some  reactive  pressure  may  be  recog- 
nized. The  limit  turbine  may  act  entirely  as  a  reaction  or  as  an 
impulse  turbine  according  to  the  conditions  under  which  it  oper- 
ates. 

127.  Condition  of  Operation. — These  wheels  operate  under  the  fol- 
lowing conditions : 

REACTION  OE  PRESSURE  TURBINES. 

Guides  complete. 

Buckets  with  restricted  outlets. 

Buckets  or  wheel  passages  completely  filled. 

Energy  most  largely  developed  through  reactive  pressure. 

Discharge  usually  below  tail  water  or  into  a  draft  tube. 

ACTION   OR  IMPULSE   TURBINES. 

Guides  partial  or  complete. 
Buckets  with  outlets  free  and  unrestricted. 
Wheel  passage  never  filled. 
Energy  entirely  due  to  velocity. 
Discharge  must  be  above  tail  water. 

No  draft  tube  possible,  except  with  special  arrangement  which 
will  prevent  contact  of  tail  water  with  wheels. 

LIMIT    TURBINES. 

(A)  Buckets  so  designed  that  the  discharge  is  unrestricted  when 
above  tail  water. 

Buckets  in  this  case  are  just  filled.    Act  without  reactive  effect. 
Discharge  above  tail  water. 

(B)  If  tail  water  rises  to  buckets,  the  discharge  is  restricted  and 
reaction  results. 

In  this  case  the  full  bucket  admits  reaction  and  discharge  may  be 
below  tail  water. 

128.  Relative  Advantage  of  Reaction  and  Impulse  Turbines.— 
The  reaction  wheel  is  better  adapted  for  low  and  moderate  heads, 
especially  when  the  height  of  the  tail  water  varies  and  where  the 
amplitude   of  such   variation   is   a   considerable   percentage   of   the 
total  head.     Such  a  wheel,  which  is  designed  to  operate  with  the 
buckets  filled,  can  be  set  low  enough  to  utilize  the  entire  head  at 


246  Water  Wheels. 

all  times  and  will  operate  efficiently  when  fully  submerged.  The 
reaction  wheel  can  therefore  be  set  to  utilize  the  full  head  at  time 
of  low  tail  water  and  when  the  quantity  of  flow  is  limited.  For 
low  head  developments  this  is  an  important  factor.  The  impulse 
turbine,  on  the  other  hand,  must  have  a  free  discharge  and  must 
therefore  be  set  far  enough  above  the  tail  water  to  be  free  from  back 
water  if  it  is  to  be  operated  at  such  times. 

Another  difference  between  the  reaction  and  the  impulse  turbine 
is  the  higher  speed  with  which  the  former  operates.  This  is  often 
a  distinct  advantage,  for  direct  connection  with  high  speed  ma- 
chinery, and  with  low  and  moderate  heads.  On  the  other  hand, 
with  high  heads  the  slower  speed  of  the  impulse  wheels  is  frequently 
of  great  advantage,  especially  in  the  form  of  the  tangential  wheel 
when  the  diameter  can  be  greatly  increased  and  very  high  heads 
utilized  with  moderate  revolutions.  In  such  cases  the  height  of 
the  back  water  is  usually  but  a  small  percentage  of  the  total  head, 
and  the  loss  due  to  the  higher  position  of  the  wheel  is  compara- 
tively small. 

The  speed  of  a  wheel  for  efficient  service  is  a  function  of  the  ratio 
of  the  peripheral  velocity  of  the  wheel  to  the  spouting  velocity  of 
water  under  the  working  head.  This  ratio  will  vary  from  .65  to  .95 
in  reaction  turbines,  according  to  the  design  of1  the  wheel.  In  im- 
pulse turbines  this  ratio  varies  from  .40  to  .50. 

129.  Relative  Turbine  Efficiencies. — The  impulse  turbine  has  the 
further  advantage  of  greater  efficiency  under  part  gate, — that  is, 
at  less  than  its  full  capacity.  When,  as  is  usually  the  case,  a  wheel 
must  operate  under  a  variable  load  it  becomes  necessary  to  reduce 
the  discharge  of  the  wheel  in  order  to  maintain  a  constant  speed 
with  the  reduced  power  required.  (See  Fig.  131).  This  is  ac- 
complished by  a  reduction  in  the  gate  opening  which  commonly 
greatly  affects  the  economy  of  operation. 

The  comparative  efficiencies  of  various  types  of  the  turbines  are 
shown  in  Fig.  131.  The  maximum  efficiency  of  turbines  when 
operated  at  the  most  satisfactory  speed  and  gate  will  be  about  the 
same  for  every  type,  if  the  wheel  is  properly  designed  and  con- 
structed and  the  conditions  of  operation  are  suitable  for  the  type 
used.  This  maximum  efficiency  may  vary  from  75  to  85  per  cent., 
or  even  between  wider  limits,  but,  with  suitable  conditions,  should 
not  be  less  than  80  per  cent.  In  order  to  make  the  curves  on  the 
diagram  truly  comparative,  the  percentage  of  maximum  efficiency 


Relative  Turbine  Efficiencies. 


247 


20 


30  40  50  60  70 

PER    CENT   OF    MAXIMUM    DISCHARGE 


80 


90 


100 


Fig.  131— Comparative  Efficiencies  of  Various  Types  of  Turbines. 

-and  of  maximum  discharge  are  plotted  instead  of  the  actual  effi- 
ciencies and  actual  discharge. 

The  Fourneyron  turbine  usually  shows  very  poor  efficiencies  at 
part  gate  as  shown  in  Fig.  131.  The  curve  for  this  turbine  is 
•drawn  from  Francis'  test  of  the  Tremont  (Fourneyron)  turbine 
{see  Fig.  132,  also  Table  LXI)  and  is  substantiated  by  efficiency 
•curves  shown  by  various  tests  by  James  Emerson.* 

The  Janval  turbines  usually  show  better  part  gate  efficiencies 
than  the  Fourneyron  but  are  not  as  efficient,  under  such  conditions, 
as  turbines  of  the  inward  flow  or  Francis  type.  The  Jonval  curve, 
shown  in  Fig.  131,  is  plotted  from  the  test  made  in  1884  at  the 


See  "Hydrodynamics"  by  James  Emerson. 


248  Water  Wheels. 

Holyoke  testing  flume  *  of  a  3O-inch  regular  Chase-Jonval  turbine. 
(See  Table  LXXVI). 

The  American-Francis  turbine  varies  greatly  in  part  gate  effi- 
ciency according  to  the  details  of  design  and  the  relation  of  speed 
and  head  under  which  it  operates.  The  curve  shown  in  Fig.  131,. 
representing  this  type,  is  from  the  test  of  a  wheel  manufactured  by 
J.  &  W.  Jolly  of  Holyoke,  Massachusetts,  similar  but  not  the  same- 
as  that  illustrated  by  the  characteristic  curve  Fig.  249. 

The  impulse  wheels  when  properly  designed  and  operated  show 
a  higher  part  gate  efficiency  than  any  other  type  of  wrheel.  The 
curve  shown  in  Fig.  131  is  from  a  test  o.f  a  12"  Doble  tangential 
wheel  in  the  laboratory  of  the  University  of  Wisconsin.! 

As  already  indicated,  the  design  of  the  wheel  has  a  great  in- 
fluence on  its  efficiency  at  part  gate.  Individual  wheels  or  series 
of  wheels  of  any  type  may  therefore  depart  widely  from  the  curves- 
above  shown,  which  are  intended  only  to  show  as  fairly  as  possible 
the  usual  results  obtained  from  well  made  wrheels  of  each  type. 

It  should  be  noted  also  that  efficiency  is  only  one  of  the  factors- 
influencing  the  choice  of  a  wheel  and  that  many  other  factors,  must 
be  weighed  and  carefully  considered  before  a  type  of  wheel  is  se- 
lected as  the  best  for  any  particular  set  of  conditions. 

130.  Turbine  Development  in  the  United  States. — The  develop- 
ment of  the  turbine  in  the  United  States  has  been  the  outgrowth 
of  some  seventy  years  of  practical  experience.  In  the  early  settle- 
ment of  the  country  the  great  hydraulic  resources  afforded  facili- 
ties for  cheap  power  and  numerous  water  powers  were  developed 
under  low  and  moderate  heads.  These  developments  created  a 
corresponding  great  demand  for  water  wheels  and  stimulated  in- 
vention and  manufacturing  in  this  line.  American  inventors  have 
devised  many  different  forms  of  wheels  which  were  patented,  con- 
structed, tested  and  improved  to  meet  the  prevailing  conditions. 
When  a  successful  wheel  was  designed,  it  was  duplicated  in  its 
original  form  and  its  proportions  increased  or  diminished,  to  con- 
form to  the  desired  capacity.  As  wheels  of  greater  capacity  or  of 
higher  speed  have  been  required,  modifications  have  been  made 
and  improved  systems  have  resulted. 

*  See  page  44  of  1897  catalogue  of  Chase  Turbine  Manufacturing  Co.. 
Orange,  Mass. 

tFrom  "Test  of  a  12"  Doble  Tangential  Water  Wheel,"  an  unpublished) 
thesis  by  H.  J.  Hunt  and  F.  M.  Johnson. 


Turbine  Development  in  the  United  States.  249 

The  best  American  water  wheel  construction  began  with  the 
Boyden-Fourneyron  and  Geylin-Jonval  turbines  of  improved 
French  design,  but  modern  American  practice  began  to  assume  its 
characteristic  development  with  the  construction  of  the  Howd-Fran- 
cis  turbines,  already  described.  Moderate  changes  in  the  form  and 
arrangement  of  buckets  and  other  details  gave  rise'  to  the  earlier 
forms' of  ''Swain/'  "Leffel"  and  "American"  wheels  each  of  which 
consisted  of  an  inward  flow  turbine  modified  from  the  earlieY  de- 
signs of  Howd  and  of  Francis  as  the  experience  of  the  inventor 
seemed  to  warrant.  In  all  of  these  cases  the  wheels  discharged 
inward  and  essentially  in  a  radial  direction  and  had  to  be  built  af 
sufficient  diameter  to  provide  an  ample  space  for  receiving  the  dis- 
charging waters.  This  necessitated  slow  speed  wheels  of  com- 
paratively low  capacity  (see  Table  I,  page  13).  In  order  to  secure 
higher  speed,  the  diameters  of  the  wheels  were  reduced  thus  re- 
ducing the  power.  This  reduction  was,  however,  more  than  coun- 
terbalanced, in  the  later  wheels,  by  an  increase  in  the  width  of 
the  bucket  in  an  axial  direction.'  It  was  found  also  that  the  cap- 
acity of  the  wheels  could  also  be  materially  increased,  with  only 
small  losses  in  efficiency,  by  decreasing  the  number  of  buckets. 
Wheels  were  gradually  reduced  in  diameter  and  the  buckets  in- 
creased in  breadth  until,  in  many  cases,  they  reached  very  nearly 
to  the  center  of  the  wheel.  This  necessitated  a  downward  dis- 
charge in  the  turbine  and  resulted  in  the  prolongation  of  the  buck- 
ets in  an  axial  direction  in  many  cases  to  almost  double  the  width 
of  the  gate.  From  this  development  has  resulted  the  construction 
of  a  series  of  wheels  known  as  the  "American  turbines"  having 
higher  speed  and  greater  power  than  has  been  reached  in  Euro- 
pean practice. 

The  entire  line  of  development  has,  until  within  the  last  fifteen 
years,  been  toward  the  increase  of  speed  and  power  for  low  and 
moderate  head  conditions.  It  is  only  within  this  period  that  a  con- 
siderable demand  has  been  felt  in  this  country  for  turbines  having 
other  characteristics  and  adapted  for  higher  heads. 

The  American  type  of  turbine,  in  its  modern  form  is  not  designed 
or  suitable  for  high  heads  its  origin  being  the  result  of  entirely 
different  conditions.  About  1890  came  a  demand  for  turbine  wheels 
under  comparatively  high  heads  which  manufacturers  of  wheels  of 
the  American  type  were  therefore  poorly  equipped  to  meet.  The 
first  of  such  wheels  supplied  were  therefore  of  European  types, 

15 


250  Water  Wheels. 

which  apparently  better  suited  such  conditions.  Recognizing, 
however,  the  importance  of  meeting  such  demands,  the  American 
manufacturer  found  that  the  wheels  of  essentially  the  original 
Francis  type  were  well  suited  for  this  purpose.  The  narrow  wheel 
and  numerous  buckets  of  the  earlier  types  reduced  the  discharge  of 
water,  and,  increasing  the  diameter,  reduced  the  number  of  revo- 
lutions. Such  types  of  wheels  of  high  efficiency  can  now  be 
obtained  from  the  leading  manufacturers  in  the  United  States,  and, 
while  many  manufacturers  still  prefer  to  furnish  simply  their  stock 
designs,  which  are  only  suited  for  the  particular  conditions  for  which 
they  were  designed,  still,  other  manufacturers  are  prepared  to 
furnish  special  wheels  which  are  designed  and  built  for  the  particu- 
lar conditions  under  which  they  are  to  be  used. 

The  systems  of  wheels  offered  by  American  manufacturers,  which 
can  be  readily  and  quickly  duplicated  at  a  much  less  expense  than 
would  result  from  the  design  of  special  wheels  for  each  particular 
customer,  has  resulted  in  the  ability  of  American  manufacturers  to 
furnish  water  wheels  of  a  fairly  satisfactory  grade  and  at  a  cost 
which  would  have  been  possible  in  no  other  way.  In  the  United 
States  the  cost  of  labor  has  been  comparatively  high  and  special 
work  is  particularly  expensive,  much  more  so  than  in  Europe  where 
skilled  mechanics  receive  a  compensation  for  labor  which  is  but 
a  small  fraction  of  that  of  their  American  competitors.  Average 
American  practice,  at  the  present  time,  leaves  undoubtedly  much 
to  be  desired  and  considerable  advance  may  be  expected  from  the 
correction  of  designs,  resulting  from  practical  experience  and  by  the 
application  of  scientific  analysis. 

131.  The  American  Fourneyron  Turbine. — As  noted  in  Chapter 
I,  one  of  the  first  reaction  turbines  developed  in  the  United  States 
was  the  Bo)^den  wheel  of  the  Fourneyron  type. 

In  these  wheels  (see  Fig.  132)  the  water  entered  from  the  center, 
guided  by  fixed  curve  guides,  g,  (Fig.  133)  and  discharged  outward 
through  the  buckets,  B.  The  use  of  these  wheels  gradually  spread 
and  they  rapidly  replaced  many  of  the  old  overshot  and  breast 
wheels  used  up  to  that  time,  and  soon  became  the  foremost  wheel 
in  New  England. 

The  manufacture  of  the  Fourneyron  turbine  has,  for  common 
use,  been  discontinued  on  account  of  the  competition  of  other 
cheaper  wheels  which  were  found  to  be  more  efficient  at  part  gate 


The  American  Fourneyron  Turbine. 


251 


Fig.   132. — Tremont    (Boyden-Fourneyron)    Turbine   (after  Francis). 


Fig.  133.— Guides  and  Buckets  of  Tremont  (Boyden-Fourneyron)   Turbine. 


252  Water  Wheels. 

and  more  generally  satisfactory  under  ordinary  conditions  of  serv- 
ice. 

The  Fourneyron  turbine,  when  well  designed  and  constructed,  is 
a  turbine  of  high  full  gate  efficiency.  This  wheel  is  adapted  for 
high  heads  where  a  comparatively  slow  speed  is  desired, — and  it 
is  now  frequently  used  for  high  grade  and  special  work  where  its 
peculiarities  seem  best  suited  to  such  conditions. 

One  of  the  modern  applications  of  the  Fourneyron  turbine  is 
that  in  the  power  plant  of  The  Niagara  Falls  Water  Power  Com- 
pany. Fig.  134  shows  vertical  and  horzontal  sections  of  one  of  the 
double  Fourneyron  units  used  by  this  company  in  their  first  plant. 
These  wheels  discharge  430  cubic  feet  per  second  and  make  250 
revolutions  per  minute ;  at  75  per  cent,  efficiency  each  wheel  will 
develop  5,000  horse  power.  The  buckets  of  these  wheels  are  di- 
vided vertically  into  three  sections  or  stories  in  order  to  increase 
their  part  gate  efficiencies.  These  wheels  are  of  Swiss  design  by 
the  firm  of  Faesch  and  Picard  and  were  built  by  The  I.  P.  Morris 
Company  of  Philadelphia.  [The  wheels  are  vertical  and  connected 
by  vertical  shafts,  each  with  one  of  the  dynamos  in  the  station 
above.  The  shaft  is  built  of  three-quarter  inch  steel,  rolled  into 
tubes  38  inches  in  diameter.  At  intervals  the  shafts  pass  through 
journal  bearings,  or  guides,  at  which  points  the  shafts  are  reduced 
to  ii  inches  in  diameter  and  are  solid.  The  speed  gates  of  these 
wheels  are  plain  cylindrical  rims  which  throttle  the  discharges 
on  the  outside  of  the  wheels  and  which,  with  the  co-operation  of 
the  governor,  keeps  the  speed  constant  within  two  per  cent  under 
ordinary  conditions  o«f  operation.  Another  wheel  of  this  type  is 
that  manufactured  and  installed  at  Trenton,  Falls,  N.  Y.,  by  the 
same  firm.  (See  Fig.  311.) 

132.  The  American  Jonval  Turbine. — The  Jonval  turbine,  orig- 
inally of  French  design,  was  introduced  into  this  country  about 
1850  and  became  one  of  the  most  important  forms  of  turbine  of 
early  American  manufacture.  In  the  tests  of  turbines  at  Phila- 
delphia in  1859-60  (see  page  360)  a  Jonval  turbine  developed  the 
highest  efficiency  and  the  type  was  adopted  by  the  city  for  use  in 
the  Fairmount  Pumping  Station.  Like  the  Fourneyron  turbine, 
these  wheels,  while  highly  efficient  at  full  gate,  have  largely  been 
superceded  by  other  cheaper  and  more  efficient  part  gate  types, — 
except  for  special  conditions. 


The  American  Jonval  Turbine. 


253 


Pig.  134.— Double  Fourneyron  Turbine  of  The  Niagara  Falls  Water  Power 
Company.     (Designed  by  Faesch  &  Picard;  built  by  I.  P.  Morris  &  Co.) 


254 


Water  Wheels. 


Fig.  135  shows  the  Geylin-Jonval  turbine  as  manufactured  by 
the  R.  D.  Wood  Company  of  Philadelphia.  W  represents  the  run- 
ner, B  the  buckets  which  receive  the  water  through  the  guides,  g. 
The  wheel  shown  has  double  inlets  that  are  closed  by  the  double 

cylinder  gates,  GG.  This 
gate  closes  up  against  the 
hood,  C,  by  means  of  the 
rod  r,  r,  which  connect 
with  the  governor  mech- 
anism. The  general  de- 
sign of  the  ordinary  wheel 
of  this  type  is  perhaps 
best  shown  by  Fig.  136.* 
In  this  figure  A  is  the 
fixed  or  guide  wheel  and 
B  is  the  movable  or  tur- 
bine runner. 

In  the  later  hydraulic 
developments  the  use  of 
this  -wheel  has  been  con- 
fined, largely  at  least, 
to  locations  that  require 
special  designs.  One 
of  the  later  develop- 
ments of  the  Jonval  tur- 
bine has  been  that  for 
The  Niagara  Falls  Paper 
Company.  The  first  in- 
stallation consisted  of  three  upward  discharge  Jonval  turbines  of 
1,100  horse  power  each,  under  a  head  of  140  feet.  The  installation 
provided,  however,  for  a  total  installation  of  six  turbines.  The  ver- 
tical shafts  are  10  inches  in  diameter  and  140  feet  in  length  and 
weigh  about  19  tons  each.  These  shafts,  in  addition  to  the  weight 
of  the  wheels, — which  are  4'  8"  in  diameter,  are  supported  by  marine 
thrust  bearings,  under  the  beveled  wheels,  together  with  a  step 
bearing  under  the  turbine.  When  the  turbine  is  in  use,  however, 
the  weight  of  the  wheel  and  the  shaft  is  balanced  by  the  upward 
pressure  of  the  water  which  at  two-thirds  gate  is  designed  to  ex- 
actly balance  this  weight.  At  full  gate  there  is  an  unbalanced  up- 


Fig.     135.— Vertical     Geylin-Jonval     Turbine 
(Manufactured  by  R.  D.  Wood  &  Co.). 


*  See  page  7,  1877  catalogue,  J.  L.  &  S.  B.  Dix,  Glen  Falls,  N.  Y. 


The   American  Jonval  Turbine. 


255 


ward  pressure,  and,  at  less  than  two-thirds  gate,  an  unbalanced 
downward  pressure;  these  pressures  are,  however,  only  the  differ- 
ence between  the  weights  and  the  water  pressure  and  are  easily 
cared  for  by  the  bearings  above  described. 

These  wheels  have  thirty  open- 
ings and  operate  at  260  revolu- 
tions per  minute.  The  gates  are 
provided  with  sleeves  (cylinder 
gates)  each  weighing  2,800  pounds 
and  slide  outside  the  guide  wheels 
to  the  hood.  These  sleeves  are 
guided  by  four  rods  which  extend 
above  the  turbine  casing  about  10 
feet  to  a  yoke  which  is  counter- 
balanced. A  sectional  view  of 
one  of  these  turbines  is  shown  in 
Fig.  137  and  the  general  arrange- 
ment of  the  plant  is  shown  in  Fig. 
138. 

A  still  more  recent  type  of  the 
Jonval  turbine  is  the  double,  hor- 
izontal wheel,  built  for  The  Niag- 
ara Falls  Hydraulic  Power  and 
Manufacturing  Company  and  in- 
stalled in  1898.  (See  Figs.  139, 
140).  These  wheels  have  a  common,  central  intake  and  quarter- 
turned  draft  tube  which  turns  down  to  and  is  sealed  in  the  tail 
race  below  the  floor.  The  speed  control  is  effected  by  a  register 
gate  through  which  the  water  passes  before  it  reaches  the  guide 
ring.  This  is  said  to  give  a  somewhat  lower  efficiency  at  part  gate 
than  does  a  gate  interposed  between  the  guide  tubes  and  runner 
bucket.  Economy  of  water  at  part  gate  is  said  to  be  no  particular 
object  in  this  plant  and  reduced  efficiency  is,  in  fact,  an  advantage 
in  that  it  reduces  the  gate  movement  and  retains  a  velocity  in  the 
penstock,  with  a  given  change  of  load,  and  consequently  reduces 
the  inertia  action  and  aids  the  speed  regulation.  This  turbine  is 
rated  at  2,500  H.  P.  at  250  revolutions  per  minute,  under  the  normal 
head  of  210  feet.* 


Fig.  13G.— Jonval  Turbine  as  Manu- 
factured by  J.  L.  &  S.  B.  Dix. 


*  See  "The  Electrical  World,"  January  14,  1899. 


256 


Water  Wheels. 


Fig.  137. — Geylin-Jonval  Turbine  of  Niagara  Falls  Paper  Mill  Co.     Manufac- 
tured by  R.  D.  Wood  &  Co.     (From  Eng.  News,  Apr.  5,  1894.) 

133.  The  American  Type  of  Reaction  Turbine. — The  Howd 
Wheel  (Fig.  13)  from  which  the  idea  of  the  Francis  inward  flow 
wheel  (Fig.  12)  was  derived,  was  invented  in  1838  and  acquired  a 
considerable  market  throughout  New  England.  From  these  wheels 
originated  the  American  inward  and  downward  or  mixed  flow  tur- 
bines. 

The  early  wheels  of  American  manufacture  were  designed  very 
much  after  the  style  of  the  Francis  wheel  with  changes,  more  or 
less  radical,  in  the  shape  and  details  of  the  buckets.  The  demand 
for  wheels  of  greater  power,  and  -higher  speed,  has  resulted  in  a 
gradual  development  of  other  and  quite  different  forms. 

The  development  of  the  turbine  in  the  United  States  is  well 
illustrated  by  that  of  the  "American"  turbine  of  Stout,  Mills  & 
Temple,  now  The  Dayton  Globe  Iron  Works  Co.  This  wheel  was 


The  American  Jonval  Turbine. 


257 


Fig.  138.— Plant  of  the  Niagara  Falls 
Paper  Co.  Showing  Installation  of 
Jonval  Turbines.  (From  Gassier' s 
Magazine,  Nov.,  1904. 


designed  in  1859  and  was  called   '' 
the    American    Turbine.      The 
general  form  of  the  original  tur- 
bine wheel  is  shown  in  Fig.  141. 

This  was  followed  (1884)  by 
the  design  of  what  is  known  as 
the  "New  American"  turbine, 
illustrated  by  Fig.  142.  In  this 
wheel  the  buckets  are  length- 
ened downward  and  have  a 
partially  downward  as  well  as 
inward  discharge. 

This    wheel  was   followed   in 
1900   by   the   "Special  New 
American"    illustrated  in    Fig.    * 
143,  having  a  great  increase  in 
capacity  and  power. 

The  fourth  and  most  recent 
type  (1903)  is  the  "Improved 
New  American"  illustrated  in 
Fig.  144.  The  comparative 
power  and  speed  of  these  vari- 
ous wheels  is  shown  in  the 
tables  on  pages  258  and  259. 

Table  XXIII  is  misleading  to 
the  extent  that  while  the  diam- 
eter of  each  wheel  is  given  as 
48"  such  diameters  are  not 
strictly  comparative.  Part  of 
the  additional  capacity  and 
power  of  the  "Special  New 
American"  and  of  the  "Im- 
proved New  American"  is  due 
to  the  cutting  back  of  the  buck- 
ets (see  Figs.  141  to  144)  which, 
while  it  reduces  the  diameter 
at  the  point  of  measurement, 
gives  a  discharge  which  would 
be  fairly  comparative  with 
wheels  of  the  older  type  of  per- 
haps three  or  four  inches  larger 
diameters.  (See  Sec.  140.) 


258 


Water  Wheels. 


TABLE  XXIII 

Development  of  "American"  Turbines.— Capacity,  Speed  and  Power  of  a 
Turbine  under  a  16-foot  Head. 


Year 
brought  out. 

Discharge 
in  cu.  ft. 

Eev.  per 
min. 

Horse 
power. 

1859 

3271 

102 

79.1 

Standard.  New  American  

1884 

5864 

102 

141.8 

New  American 

1894 

9679 

107 

234  0 

Special  New  American  
Improved.  New  American         .... 

1900 
1903 

11061 
13234 

107 
139 

267.0 
3^5.0 

Fig.    139. — Horizontal    Geylin-Jonval    Turbine   of  Niagara  Falls  Hydraulic- 
Power  &  Manufacturing  Co.     Showing  Guide  Chutes.* 


*  Cuts  139  and  140  reproduced  from  Electrical  World,  Jan.  14,  1899.     Tur- 
bines manufactured  by  R.  D.  Wood  &  Co. 


The  American  Type  of  Reaction  Turbine. 


259 


The  development  of  turbines  may  also  be  illustrated  by  a  compar- 
ison of  the  size  and  speed  of  turbines  of  various  series  required  to 
develop  essentially  the  same  power.  (See  Table  XXIV.) 

TABLE  XXIV 
Increase  in  Speed  of  "American"  Turbines  for  Same  Power  (16-foot  head). 


Size  of 
wheel. 

Horse 
power. 

R.  P.  M. 

48 

79.1 

102 

New  American                                                  

36 

81.5 

136 

27^ 

87.3 

186 

Imprcw6(l  New  American                                    .... 

25 

87.5 

267 

Fig.  140. -Horizontal  Geylin-Jonval  Turbine  Showing  Bucket  Ring* 


Figs.  145  and  146  show  a  vertical  and  a  horizontal  half  plan,  half 
section  of  a  vertical  Improved  New  American  turbine.  W  is  the 
crown  and  hub  of  the  wheel;  B,  the  buckets;  G,  G,  are  the  wicket 


*See  foot  note  raSe  258» 


260 


Water  Wheels. 


gates  that  control  the  admission  of  water  to  the  wheels  and  which 
are  operated  by  means  of  the  ring  Gr,  which  is  moved  by  an  eccen- 
tric and  rod,  r,  connected  with  the  governor  through  the  shaft,  P. 

The  inner  edges  of  the  bucket  are  spaced  some  distance  from  the 
shaft  and  the  main  discharge  is  inward  and  downward,  though  a 
portion  of  the  bucket  will  admit  of  a  slightly  outward  discharge. 

134.  The  Double  Leffel  Turbine. — Perhaps  the  greatest  depar- 
ture of  American  inventors  from  the  lines  of  the  original  Francis 


Fig.  142. — New  American 
Turbine  Runner. 


Fig.    141. — American    Turbine   Run- 
ner.* 

TABLE  XXV. 

Development  of  "Leffel"  Wheel. — Capacity,  Power  and  Speed  of  40-inch 
Wheel  Under  16-foot  Head. 


Year 
brought  out. 

Discharge. 

Kev.  per 
minute. 

Horse 
power. 

Standard  

1860 

2547 

138 

Special  

1870 

3672 

138 

93 

1890 

6551 

158 

155 

Improved  Samson  

1897 

8446 

163 

207 

*  Manufactured  by  The  Dayton  Globe  Iron  Works  Co. 


The  American  Type  of  Reaction  Turbine.  261 


Fig.  143.— Special  New  American  Turbine 
Runner.* 


Fig.    144. — Improved    New   American   Tur- 
bine Runner.* 


type  of  turbine  was  that 
of  James  Leffel.  In  this 
wheel  was  combined  a 
double  runner,  the  upper 
half  being  a  radial  inflow 
runner  of  the  Francis  type 
and  the  lower  half  con- 
sisting of  a  runner  with 
inward  radial  admission 
and  axial  discharge,  es- 
sentially on  the  line  of  the 
later  development  of  tne 
American  type  of  wheels. 
The  wheel,  as  originally 
designed,  had  the  narrow 
bucket,  slow  speed  and 
low  power  of  all  early 
American  wheels.  In  its 
later  development  the 
buckets  have  been  extend- 
ed inward  and  downward 
and  these  wheels  have 
found  their  best  modern 
development  in  the  Sam- 
son-Leffel  wheel,  illustrat- 
ed in  Figs.  147  to  151. 

In  Fig.  147,  W  repre- 
sents the  hub  and  crown 
of  the  wheel  which  is  se- 
curely keyed  to  the  shaft, 
S.  B'  B'  are  the  upper 
buckets  that  discharge 
inward  and  downward 
through  the  passage  aa. 
The  lower  buckets,  BB, 
it  will  be  noted,  have  the 
same  lines  as  other  modern 
wheels  of  the  American 
type.  They  receive  the 


*  Manufactured  by  The  Dayton  Globe  Iron  Works  Co. 


262 


Water  Wheels, 


Pigs.  145  and  146.— Section  and  Plan  of  ImprovedNew  American  Turbine.* 


*  Manufactured  by  The  Dayton  Globe  Iron  Works  Co. 


The  American  Type  of  Reaction   Wheels.  263 


Figs.   147   and   148.— Section   and   Plan  of  Samson  Turbine.* 


Manufactured  by  The  James  Leffel  &  Co. 


264 


Water   Wheels. 


Figs.  149,  150  and  151. — Top  View,  Runner  and  Outside  View  of  Samson  Tur- 
bine.* 


*  Manufactured  by  The  James  Leffel  &  Co. 


The  Double  Leffel  Turbine. 


265 


water  inward  and  discharge  it  downward,  outward  and  inward  with 
the  general  purpose  of  distributing  it  over  the  cross-section  of  the 
turbine  tube.  The  gates,  G,  are  of  the  wicket  type  and  are  con- 
nected by  rods  with  an  eccentric  circle  which  is  operated  through 
the  arm,  A,  and  the  gearing,  Gr,  by  the  governor  shaft,  P.  The 
gate  gearing  is  well  shown  by  reference  to  the  section-plan,  Fig. 
148,  and  the  top  view,  Fig.  149. 

The  Samson  turbine  runner  is  illustrated  in  Fig.  150,  and  Fig. 
151  shows  an  outside  view  of  one  of  the  vertical,  turbine  units. 


Fig.  152.— Double  Horizontal  Leffel  Turbine  of  The  Niagara  Falls  Hydraulic 
Power  &  Manufacturing  Co.    Manufactured  by  The  James  Leffel  &  Co. 

The  development  of  this  wheel  is  illustrated  by  Table  XXV.  This 
table  is  fairly  representative  of  the  growth  of  this  turbine  as  the 
diameter  is,  in  all  cases,  the  maximum  diameter  of  the  wheel.  (See 

Sec.  140.) 

The  adaptability  of  the  earlier  turbine  designs  to  the  later  mod- 
erate head  developments  is  well  illustrated  in  the  design  of  the 
16 


266 


Water  Wheels. 


wheels  for  The  Niagara  Falls  Hydraulic  Power  and  Manufacturing 
Company,  installed  by  The  James  Leffel  Company  about  1892. 
These  turbines  have  the  single  narrower  buckets,  smaller  discharge 
and  relatively  slower  speed  of  the  earlier  designs.  The  runners  are 
double  discharge,  horizontal,  seventy-four  inches  in  diameter  and 
operate  at  a  speed  of  250  revolutions  per  minute  under  a  head  of 
215  feet,  and  each  wheel  develops  about  3,500  horse  power. 


Fig.  153. — Leffel  Double  Runner  of  The  Niagara  Falls  Hydraulic  Power  & 
Manufacturing  Co.     Manufactured  by  The  James  Leffel  &  Co. 

Fig.  152  shows  one  of  these  units  complete.  Fig.  153  is  a  view 
of  the  runner.  For  a  test  of  this  wheel,  made  December  1903,  see 
page  381. 

J35-  Other  American  Wheels. — The  development  of  modern 
American  wheels  could,  perhaps,  have  been  equally  well  illustrated 
by  the  growth  of  various  other  American  turbines.  The  develop- 
ment of  all  American  wheels  up  to  the  present  time  has  been  on 
the  line  of  increasing  both  the  speed  and  the  power  of  the  wheel 
for  low  head,  with  a  return  to  the  earlier  type  for  wheels  to  be  used 
under  the  moderate  heads. 

Fig.  154  illustrates  a  runner  of  the  well-known  McCormick  pat- 
tern. Mr.  J.  B.  McCormick,  who  had  previously  become  familiar 


Other  American  Wheels. 


267 


with  certain  wheels  of  large  capacity  designed  and  patented  by 
Matthew  and  John  Obenchain,  re-designed  and  improved  these 
wheels,  about  1876,  and  secured  high  efficiencies  together  with 
increased  power  far  beyond  any  other  wheels  of  that  period.  Mc- 

Cormick  wheels  in  their 
original  or  modified  form 
are  now  made  by  a  large 

If  j|r&  number  of  American  man- 

|  uTacturers     and     these 

wheels  have  had  a  marked 
effect  on  the  design  of 
almost  all  modern  Ameri- 
can water  wheels.  The 
runner  in  the  illustration 
is  the  Hunt-McCormick 
runner  as  manufactured  by 
The  Rodney  Hunt  Ma- 
chine Company,  but  is 
very  similar  to  the  Mc- 


Fig.  154. — Hunt-McCormick  Runner  of  The 
Rodney  Hunt  Machine  Co. 


Cormick  wheels  of  various 
other  manufacturers. 

The  Smith-McCormick 
runner  is  manufactured  by 
The  S.  Morgan  Smith 
Company.  This  company 
has  also  recently  brought 
out  a  new  wheel  called 
the  "Smith  Turbine/' 
of  greater  power  and 
higher  speed,  the  runner 
of  which  is  illustrated  by 
Fig.  155.  Fig.  156  repre- 
sents the  Victor  runner  or 
"type  A"  runner  of  The 
Platt  Iron  Works  Com- 
pany, designed  for  low 
heads. 

Fig.  157  is  the  "typeB" 
runner,  of  the  same  Corn- 
Fig.  155.-Smith  Runner  of  S.  Morgan  pany,  designed  for  medi- 
Smith  Co. 


um    heads.       This    runner 


268 


Water  Wheels. 


again  illustrates  the  tendency  to  return  to  the  earlier  forms  of 
runner  for  medium  head  wheels.  This  latter  type  has  also  been 
adopted  by  other  manufacturers  of  turbines,  as  may  be  seen  by  ref- 
erence to  Fig.  158  which  shows  the  Hunt  runner  manufactured  for 
moderate  heads  by  The  Rodney  Hunt  Machine  Company. 

Fig.  159  is  from  a  shop 
photograph  of  the  Shawin- 
igan  Falls  turbine  manu- 
factured by  the  I.  P.  Mor- 
ris Company.  This  is  one 
of  the  largest  turbines  ever 
constructed  and  develops 
10,500  horse  power  under 
a  head  of  140  feet.  It  is  a 
double  mixed  inflow  type 
with  spiral  casing  and  a 
double  draft  tube  through 
which  the  water  discharges 
outward  from  the  center. 
The  diameter  of  the  cas- 
ing at  the  intake  is  10i 
feet  and  the  sectional 
area  gradually  diminishes 
around  the  wheel  in  pro- 
portion to  the  amount  of 
water  flowing  at  each 
point.  The  wheel  com- 
plete is  30  feet  in  height 
and  weighs  182  tons.  The 
runner,  which  is  of  bronze, 
is  shown  in  Fig.  160. 

Figs.  161  and  162  show 
two   sections    of   a    single 
turbine  of  the  Francis  in- 
flow   type    built    for    the 
Snoqualmie-Falls  plant  of 
The    Seattle    &   Tacoma 
Power  Company   by   The 
Platt    Iron    Works    Corn- 
Fig.  157. — High  Head  or  "Type  B"  Runner    pany.     The  turbine  has  9 
of  The  Platt  Iron  Works  Co.  capacity    of    about    9.000 


Fig.  156.— Victor  or  "Type  A"  Runner  of 
The  Platt  Iron  Works  Co. 


Other  American  Wheels. 


269 


H.  P.  under  270-foot  head  .at  300  R.  P.  M.  The  runner  is  66  inches 
in  diameter  and  has  a  width  of  9i  inches  through  the  buckets.* 
This  is  believed  to  be  the  largest  capacity  single  discharge  wheel 
yet  constructed. 

For  further  details  see  Figs.  183,  189  and  190. 
136.  Early  Development  of  Impulse  Wheels. — As  already  pointed 
out   (see  Chapter  I,  Figs.  6  and  7),  water  wheels  of  the  impulse 
type  were  among  the  earlier  forms  used.     In  the  practical  construc- 
tion of  water  wheels  for  commercial  purposes  in  this  country,  the 

reaction  turbine  was,  how- 
ever, the  earliest  form  of 
development.  This  was 
because  the  reaction  tur- 
bine was  best  suited  for 
the  low  heads  first  devel- 
oped. As  civilization  ad- 
vanced from  the  more  level 
country  into  the  moun- 
tainous regions  the  condi- 
tions were  found  to  radi- 
cally differ.  In  the  form- 
er location  large  quanti- 
ties of  water  under  low 
heads  were  available;  in 
the  latter,  the  streams 
diminished  in  quantity 
but  the  heads  were  enorm- 
ously increased.  These 
conditions  demanded  an  entirely  different  type  of  wheels  for  power 
purposes  and  the  demand  was  met  by  the  construction  of  the  tan- 
gential wheel  now  so  widely  and  successfully  used  in  the  high  head 
plants  of  the  West. 

The  earliest  scientific  consideration  of  impluse  wheels  in  this 
country  was  by  Jearum  Atkins  who,  apparently,  anticipated  the 
design  of  the  wheels  of  the  Girard  type  in  Europe  by  his  design  of 
such  a  wheel  in  1853.  t  (See  Fig.  163.) 


Fig. 


158. — Hunt   Runner   of   The   Rodney 
Hunt  Machine   Co. 


*  See  "Engineering  News,"  March  29,  1906. 

t  See  "Tangential  Water  Wheels"  by  John  Richards,  Cassier's  Magazine, 
vol.  v,  p.  117. 


270 


Water  Wheels. 


Fig.  159.— Shawinigan  Falls  Turbine,  Manufactured  by  I.  P.  Morris  Co. 


Other  American  Wheels.  271 

In  Atkins'  first  application  for  a  patent  (in  1853)  he  shows  a 
clear  conception  of  the  principles  of  the  impulse  wheel. 

After  describing  the  mechanical  construction  of  his  wheel,  Mr. 
Atkins  says:  "The  important  points  to  be  observed  in  the  con- 
struction of  this  wheel  and  appendages,  are :  First,  that  the  gear- 
ing *  *  *  should  be  so  arranged  as  to  allow  the  wheel's  veloc- 
ity at  the  axis  of  the  buckets  to  be  equal  to  one-half  the  velocity 
of  the  water  at  the  point  of  impact,  *  *  * 

"As  the  power  of  water,  *  *  *  is  measured  by  its  velocity, 
*  *  *  it  is  obvious  that  in  order  that  the  moving  water  may 
communicate  its  whole  power  to  another  moving  body,  the  velocity 
of  the  former  must  be  swallowed  up  in  the  latter.  This  object  is 


Fig.  1GO. — Shawinigan  Falls  Turbine  Runner. 

effected  by  the  before-described  mode  of  applying  water  to  a  wheel 
in  the  following  manner,  the  velocity  of  the  wheel,  as  before 
stated,  being  one-half  that  of  the  water. 

"Let  us  suppose  the  velocity  of  the  water  to  be  twenty-four  feet 
per  second ;  then  the  velocity  of  the  wheel  being  twelve  feet  per 
second,  the  relative  velocity  of  the  water  with  respect  to  the  wheel, 
or  the  velocity  with  which  it  overtakes  the  wheel,  will  be  twelve 
feet  per  second.  Now  it  is  proved  theoretically,  and  also  demon- 
strated by  experiment,  that  water  will  flow  over  the  entire  surface 
of  the  semi-circular  buckets  of  the  wheel  with  the  same  velocity 
with  which  it  first  impinged  against  them,  or  twelve  feet  per  sec- 
ond. Then,  as  the  water  in  passing  over  the  face  of  the  buckets 


272 


Water  Wheels. 


has  described  a  semi-circle,  and  as  its  return  motion  on  leaving 
the  wheel  is  in  an  opposite  direction  from  that  of  the  wheel,  its 
velocity  with  respect  to  the  wheel  being  twelve  feet  per  second, 
and  as  the  wheel  has  an  absolute  velocity  of  twelve  feet  per  sec- 


Fig.  161.— Section  Snoqualmie  Falls  Reaction  Turbine.     The  Platt  Iron  Works 

Company. 

ond,  it  is  obvious  that  the  absolute  velocity  of  the  water  with  re- 
spect to  a  fixed  point  is  entirely  suspended  at  the  moment  of  leav- 
ing the  inner  point  of  the  buckets,  its  whole  velocity,  and  conse- 
quently its  whole  power,  having  been  transmitted  to  the  wheel." 


Early  Development  of  Impulse   WheeL 


273 


Pig.  162. — Section-Elevation  Snoqualmie  Falls  Reaction  Turbine   (The  Platt 

Iron  Works  Co.). 


Fig.  163.— Plan  of  Atkins  Wheel  and  Wheel  Case  (1853).     From  Cassier's 
Magazine,  Vol.  v,  p.  119. 


274 


Water  Wheels. 


a.  Moore  bucket,  1874. 


6.  Knight  buckets,  1870. 


c.  Dodd  bucket,  1889. 


d.  Hug  bucket,  1897. 


e.  Doble  Ellipsoidal  bucket, 

1889.  /.  Pelton  bucket,  1880. 

Fig.  1C4. — Buckets  of  Tangential  or  Impulse  Water  Wheels.     (Trans.  Am. 
Inst.  Mining  Eng.  1899. 

Mr.  Atkins'  first  application  for  a  patent  was  rejected.  After  a 
long  illness,  from  which  he  finally  recovered,  he  again  applied  for  a 
patent  which  was  finally  granted  in  1875.  The  Atkins'  patents  are 
simply  of  historical  interest  as  his  inventions  have  had  little  effect 
on  the  practical  development  of  the  impulse  wheel. 


American  Impulse  Wheels. 


275 


137.  American  Impulse  Wheels. — The  impulse  wheel  found  its- 
earliest  practical  development  in  California  where  the  conditions  for 
the  development  of  power  made  such  a  wheel  necessary.  The 
early  tangential  wheel,  used  on  the  Pacific  Coast,  was  quite  simple 
in  construction  and  the  development  of  the  buckets,  which  began 
with  the  simpler  flat  and  curved  forms,  was  very  largely  based  on 
the  experimental  method  used  for  the  development  of  the  reaction, 


Fig.  1G5 .— Telluride  Double  Tangential  Wheels.     2000  H.  P.     500  Foot  Head. 
(Pel ton  Water  Wheel  Co.) 

turbine  in  the  East.  Experiments  were  made  at  the  University 
of  California,  by  Mr.  Ralph  T.  Brown,  as  early  as  1883,  and  the 
bulletin,  published  by  the  department  was  the  earliest  literature  on 
tangential  wheels  published  in  this  country. 

With  the  early  development  of  the  tangential  bucket  are  con- 
nected the  names  of  Knight,  Moore,  Hesse,  Pelton,  Hug,  Dodd 
and  Doble,  and  many  other  inventors,  whose  wheels  have  become 
well-known  and  widely  used.  The  most  extensive  early  develop- 


276 


Water  Wheels. 


ment  of  this  wheel  was  by  The  Pelton  Water  Wheel  Company 
whose  work  has  been  so  widely  known  and  used  as  to  make  the 
•name  "Pelton  Wheel"  a  common  title  for  all  wheels  of  the  tangen- 
tial type. 

Some  of  the  many  forms  of  American  buckets  used  are  shown  in 

Fig.  164  with  the  approximate 
date  of  their  invention  or  de- 
sign. 

The  general  arrangement  of 
a  double  2000  H.  P.  unit,  run- 
ning at  200  R.  P.  M.  under  500 
foot  head  is  shown  in  Fig.  165. 
This  is  one  of  three  units  in- 
stalled by  The  Pelton  Water 
Wheel  Company  for  The  Tellu- 
ride  Transmission  Plant  of  Col- 
orado. 

The  wheels  are  of  cast  steel 
fitted  with  steel  buckets,  held 
in  position  by  turned  steel 
bolts.  They  are  connected  by 
a  flexible  coupling  to  a  1,200 
H.  P.  generator. 

Fig.  166  shows  the  runner  of 
an  impulse  wheel  made  by  the 
same  company.  This  is  9'  10" 
in  diameter,  and  is  designed  to 
develop  5,000  H.  P.  at  225  R. 
P.  M.  under  an  effective  head 
of  865  feet. 

Fig.  167  shows  the  runner  of  an  impulse  wheel  manufactured  by 
the  Abner  Doble  Company.  This  runner  was  from  the  Doble  Wa- 
ter Wheel  Exhibit  at  the  St.  Louis  Fair  and  developed  170  H.  P. 
at  170  R.  P.  M.  under  a  head  of  700  feet  and  generated  direct  cur- 
rent for  use  on  the  intramural  railway. 

In  addition  to  the  tangential  wheels  already  described,  a  few 
manufacturers  have  developed  wheels  of  the  Girard  type.  One 
such  wheel,  designed  and  built  by  The  Platt  Iron  Works  Company, 
is  illustrated  in  Figs.  168  to  171,  inclusive.  Fig.  168  is  a  section- 
elevation  showing  the  arrangement  and  design  of  the  guides  and 


Fig.  166.— Pelton  Tangential  Water 
Wheel  Runner.  Designed  for  5000 
H.  P.  at  865  foot  head  and  225  E. 
P.  M.  (Pelton  Water  Wheel  Co.) 


American  Impulse  Wheels.  277 

buckets  of  the  wheel.  Fig.  169  shows  a  section  through  the  wheel 
and  on  the  line  of  the  shaft.  In  these  figures  W  represents  the 
runner;  BB  the  buckets;  g,  the  inlet  guides,  and  G,  the  gate  by 
which  all  or  a  portion  of  the  guide  passages  may  be  closed  and  the 
power  of  the  wheels  reduced.  The  gate,  G,  is  connected  by  the 
gearings,  Gr,  with  the  rod,  r,  which  is  connected  through  the  rocker 


Fig.  167. — Doble  Runner.     (Abner-Doble  Co.) 

arm  with  the  governor  mechanism.  The  wheel  or  runner  of  this 
turbine  is  shown  by  Fig.  170,  and  a  general  view  of  the  wheel  is 
shown  by  Fig.  171. 

138.  Turbine  Development  in  Europe.— Modern  European  tur- 
bine practice  has  been  the  development  of  the  last  twenty  years. 
European  manufacturers  have  approached  the  subject  more  on  the 


Water  Wheels. 


t>asis  of  theoretical  analysis  than  has  been  done  in  America.  The 
•conditions  of  development  have  also  been  largely  special  and  not 
under  such  uniform  conditions  as  in  America.  The  result  has  been 
the  development  of  special  designs  for  special  locations  and  the 
rapid  accumulation  of  a  considerable  experience  under  a  wide  range 


Fig.  168. — End  Section  and  Elevation,  Girard  Impulse  Turbine  with  Draft 
Tube.     (Platt  Iron  Works  Co.) 

of  conditions.  While  the  radial  flow  turbines  were  the  earlier  type 
developed,  European  practice  has  been  largely  centered  on  the  axial 
flow  wheels  of  the  Jonval  type  for  complete  turbines,  and  axial 
flow  and  radial  flow  wheels  of  the  Girard  type  for  partial  turbines 
under  high  heads.  * 


American  Impulse  Wheels. 


279 


The  axial  flow  turbine  while  simple  in  construction  and  low  in 
cost  is  difficult  to  regulate  and  hence  the  demands  of  electrical  de- 
velopment for  close  regulation  has  given  rise  to  a  variety  of  mod- 
ern designs  which  are  summarized  by  Mr.  J.  W.  Thurso  essentially 
as  follows :  * 


Fig.  169. — Longitudinal  Section  Girard  Impulse  Turbine.     (Platt  Iron  Works 

Company.) 

ist.  For  low  heads  to  20  feet.  Radial  inward  flow,  reaction  tur- 
bines with  vertical  shafts  and  draft  tubes. 

2nd.  For  medium  heads,  20  to  300  feet.  Radial  inward  flow  reac- 
tion turbines  with  horizontal  shafts  and  concentric  or  spiral  cases 
and  draft  tubes. 

3rd.  For  high  heads  over  300  feet.  Radial  outward  flow,  full  or 
partial  action  turbines  (of  the  Girard  type)  with  horizontal  shafts, 


*  See  "Modern  Turbine  Practice"  by  J.  W.  Thurso. 


280 


Water  Wheels. 


Fig.     170 — Runner   of    Girard    Turbine.     Type 
High-Pressure  Runner.  (Platt  Iron  Works  Co.) 


Fig.  171.— General  View   of   Girard  Turbine   with 
Cover  Raised.     (Platt  Iron  Works  Co.) 


often  with  draft  tubes; 
also,  modified  impulse 
wheels  of  a  tangential 
type. 

The  types  of  tur- 
bines for  low  and  mod- 
erate heads  are  mod- 
ifications of  the  Fran- 
cis inward  flow  turbine. 
Earlier  European 
practice  is  perhaps  well; 
represented  by  Fig. 
172  which  represents 
one  of  eight  turbines 
installed  by  Messrs. 
Escher,  Wyss  &  Co. 
c>  for  the  City  of  Geneva, 
Switzerland.  These 
wheels  are  of  the  Jon- 
val  type  and  operate 
under  heads  some- 
times as  great  as  12 
feet  but  during  high 
water  the  heads  de- 
crease to  about  five 
and  one-half  feet. 
The  turbines  consist  of 
three  annular  rings  or 
buckets  and  are  so  de- 
signed that  the  water 
is  admitted  to  as  many 
buckets  as  may  be  re- 
quired for  economical 
operation  under '  the 
very  great  differences 
in  the  condition  of 
supply.  The  width  of 
the  inner  and  interme- 
diate rings  are  each 
seventeen  and  three- 


Turbine  Development  in  Europe. 


281 


quarters  inches,  and  the  outer  ring  is  eleven  inches,  all  meas- 
ured radially.  The  outside  diameter  of  the  wheel  is  thirteen  feet, 
eleven  inches.  The  outer  ring  of  guides  is  not  provided  with 
means  for  excluding  the  water  from  the  buckets  but  the  intermedi- 
ate or  inner  rings  can  be  entirely  and  independently  closed.  The 


Fig.  172.— One  of  the  seventeen  210  H.  P.  Jonval  Turbines  at  the  Geneva 
Water  Works.    Built  by  Eecher,  Wyss  &  Co. 

gates  for  closing  the  intermediate  and  inner  rings  consist  of  a  flat 
plate  in  the  form  of  a  half  ring,  which  lies  on  the  top  of  the  crown 
and  a  vertical  curtain  which  hangs  from  the  end  of  the  plate  and 

completes  the  closure  of  the  other  half  of  the  bucket  the  openings 
17 


282 


Water  Wheels. 


of  which  are  on  the  side  of  the  same,  the  water  entering  the  buckets 
by  a  quarter-turn. 

These  turbines  are  used  to  operate  the  pump  that  furnishes  the 
water  supply  for  the  city  of  Geneva  for  domestic  and  manufactur- 
ing purposes. 


Fig.  173.     The  1200  H.  P.  Double  Turbine  at  Chivres  near  Geneva. 
Escher,  Wyss  &  Co.     ( Gassier' s  Magazine,  October,  1897.) 

Fig.  173  shows  a  pair  of  vertical  turbines  furnished  by  the  same 
company  for  Chivres  near  Geneva.  Here  the  fall  in  summer  is  15 
feet  and  in  winter  28  feet.  The  lower  turbine  will  develop  1,200 


Turbine  Development  in  Europe.  283 

H.  P.  at  80  R.  P.  M.  under  the  higher  head,  and  under  the  lower 
head  the  turbine  above  works  writh  the  lower  one. 

Each  turbine  is  cone  shaped  and  divided  into  three  compart- 
ments in  order  to  maintain  the  efficiency  of  the  wheels  at  the  same 
revolutions  under  the  wide  range  in  heads. 

Rapid  advancement  is  now  being  made  in  turbine  design  both  in 
this  country  and  in  Europe  and  the  progress  can  best  be  known  and 
appreciated  by  reference  to  the  current  technical  press. 


CHAPTER  XIII. 

TURBINE  DETAILS  AND  APPURTENANCES. 

139.  The  Runner — Its  Material  and  Manufacture. — The  runners 
of  most  reaction  turbines  (see  Figs.  136,  142  to  149,  151,  154  to  159, 
161)  consist  of  hubs,  crowns  and  rings,  to  which  the  buckets  are  at- 
tached. The  wheels  are  sometimes  cast  solid,  and  sometimes  built 
up.  In  built-up  wheels  the  buckets  are  first  cast,  or  otherwise 
formed,  after  which  they  are  placed  in  a  form  or  moulded,  and  the 
crowns,  hubs  and  rings  are  cast  to  them.  Turbine  water  wheels 
for  low  heads  are  usually  made  of  cast  iron  or  of  cast  iron  with 
steel  buckets.  Wheels  for  high  heads  are  frequently  made  of  cast 
bronze  or  of  cast  steel.  (See  Figs.  158  and  159.) 

Probably  the  majority  of  cast  wheels  manufactured  at  the  pres- 
ent time  are  cast  in  one  solid  casting  of  buckets,  rings,  hubs,  and 
crowns.  The  buckets  are  formed  by  carefully  prepared  cores  and 
in  such  manner  as  to  leave  them  uniform  in  spacing  and  thickness, 
and  smoothly  finished  so  as  to  admit  of  the  passage  of  water  through 
or  between  them  without  excessive  friction.  With  wheels  so  cast, 
no  material  finishing  or  smoothing  of  the  surfaces  of  the  bucket  is 
practicable,  and  the  casting  must  come  from  the  sand  with  a  satis- 
factory surface.  In  wheels  cast  solid,  great  care  is  necessary  in 
order  to  prevent  serious  shrinkage  strains.  This  is  partially  over- 
come by  the  use  of  soft  iron,  which  results,  however,  in  increased 
wear  of  runners  subject  to  the  action  of  sand-bearing  waters. 

With  buckets  cast  separately,  a  higher  surface  finish  of  the 
bucket  is  possible ;  but  when  separate  buckets  are  made  and  after- 
wards united,  the  runner  must  be  strongly  banded  in  order  to  give 
it  the  necessary  strength.  Buckets  of  sheet  steel,  forged  or  bent 
to  the  desired  shape,  present  a  uniform  and  satisfactory  surface, 
and  when  punched  at  the  edges  before  casting,  form  a  solid  and 
substantial  wheel. 

The  runners  of  Girard  impulse  wheels  (see  Fig.  171)  are  made 
in  the  same  manner  as  reaction  runners. 

The  runners  of  tangential  wheels  are  usually  made  with  separate 
buckets  and  body.  (See  Figs.  167  and  168.)  The  bodies  are  made, 


Diameter  of  Runner.  285 

according  to  the  severity  of  the  service,  of  cast  iron,  semi-steel, 
forged  steel,  etc.  The  buckets,  dependent  on  the  conditions  of 
service,  may  be  of  cast  iron,  cast  steel,  gun  metal,  bronze,  etc.  The 
buckets,  in  the  best  wheels,  are  cast,  shaped  and  polished  and  care- 
fully fitted  to  the  wheel  body.  The  bolt  holes  are  then  carefully 
drilled  and  reamed  and  the  buckets  are  bolted  in  position  by  care- 
fully turned  and  fitted  bolts. 

140.  Diameter  of  the  Runner. — The  diameters  of  reaction  runners 
are  measured  at  the  inlet,  and,  when  the  buckets  at  the  inlet  are 
parallel  and  of  one  size,  the  determination  of  the  turbine  diameter 
is  a  simple  matter.  (See  Fig.  174,  diagram  A.)  In  order  to  give 
the  runner  greater  speed  and  capacity,  the  buckets  are  sometimes 
cut  back  at  a  point  opposite  the  bottom  of  the  gate  opening  (see 
diagram  B),  and  the  diameter  of  the  runner  opposite  to  the  gates  is 
reduced  below  that  of  the  lower  diameter.  In  such  cases  the  edges 
of  the  buckets  are  sometimes  made  parallel  with  the  shaft  but  are 
usually  inclined  upward.  In  the  latter  case,  the  diameter  of  the 
wheel  at  its  top  may  be  considerably  reduced  over  its  diameter  at 
the  offset.  In  such  cases  the  cutting  back  of  the  runner  may  be  one 
or  more  inches  at  the  bottom  line  of  the  gate  with  an  inch  or  more 
inclination  to  the  top  of  the  buckets,  and  the  diameter  of  the  wheel 
at  D  and  D'",  diagram  B,  may  differ  from  two  to  six  inches  or  even 
more. 

With  wheels  so  constructed,  there  is  considerable  difference  in 
the  practice  of  different  manufacturers  in  measuring  and  listing  the 
diameter  of  the  wheels  made  by  them.  In  some  cases,  the  inside 
diameter,  from  rjng  to  ring,  D,  diagram  B,  of  the  runner,  is  given 
as  the  list  diameter.  In  other  cases,  the  diameter  is  taken  at  the 
inner  angle  of  the  offset  as  D'.  In  a  number  of  cases  the  diameter  is 
measured  at  about  the  center  of  the  gateway,  D",  and  in  other  cases, 
the  diameter  is  measured  at  the  upper  and  smaller  diameter  of  the 
runner,  D"'.  This  variable  practice  leads  to  a  considerable  differ- 
ence in  the  nominal  diameter  of  the  various  turbines  as  listed  in 
the  catalogues,  and  frequently  a  runner  listed  as  of  a  certain  diame- 
ter by  one  manufacturer  may  be  two  to  six  inches  larger  than  the 
runner  of  another  manufacturer  which  is  listed  as  of  the  same  di- 
ameter. This  discrepancy  in  the  method  of  measuring  and  listing 
the  diameter  of  turbine  runners  accounts,  in  some  degree,  for  the 
apparent  greater  capacity,  higher  speed  or  greater  power  of  the 
wheels  of  one  manufacturer  over  those  of  another. 


286 


Turbine  Details  and  Appurtenances. 


The  practice  of  some  of  the  American  manufacturers  of  turbines, 
in  measuring  and  listing  the  diameters  of  their  wheels,  is  shown 
in  Table  XXV.  In  this  table,  all  runners  which  are  not  cut  back 
and  with  edges  parallel  to  the  shaft,  are  classified  as  Style  A,  even 
where  they  differ  widely  from  the  form  shown  in  diagram  A,  Fig. 
174. 

All  runners  with  buckets  cut  back  are  classified  as  Style  B,  even 
where  the  bucket  edges  are  parallel  with  the  shaft. 

The  diameters  of  tangential  runners  are  usually  measured  be- 
tween the  centers  of  buckets  or  on  the  diameter  of  the  circle  on 
which  the  center  of  the  jet  impinges  on  the  buckets. 


TABLE  XXV. 

Practice  of  Various   American   Manufacturers  i>i   Measuring  and  Cataloging 
the  Diameter  of  Turbine  Water  Wheels. 


Manufacturer. 

Name  of  Kunner. 

Style. 

Point  of 
measure- 
ment. 

Dayton  Globe  Iron  Works 

American  

A 

j) 

New  American  

A 

D 

Rodney  Hunt  Machine  Co  .  . 

Special  New  American  
Improved  New  American1  .  . 
McCormick8 

B 
B 
B 

\y 

D' 
j) 

Hunt  

A 

D 

The  James  Leffel  &  Co  

Standard  Leffel  

A 

D 

Special  Leffel 

A 

p 

Samson 

B 

D 

Platt  Iron  Works  Co  

Improved  Samson  
Type  A  

B 
B 

D 
D" 

Tvpes  B  and  C  

A 

D 

S  Morgan  Smith  Co  

McCormick3 

B 

D' 

Smith 

B 

D' 

The  Trump  Manufacturing  Co. 

Standard  Trump4   

B 

jy, 

Hisrh  Speed  Trump  

B5 

P 

Wellman,  Seaver,  Morgan  Co 

Jolly-McCormick 

B 

D" 

1  Fillet  at  angle.     Diameter  measured  just  above. 

2 Diameter  of  Hunt-McCormick  runners  as  measured  at  the  crown  which  pro- 
jects beyond  the  tips  of  the  buckets  and  is  essentially  the  same  in  diameter  as  at  D' 

3Diameter  of  the  Smith-McCormick  runners  is  measured  at  the  crown  which 
projects  beyond  the  tips  of  the  buckets  and  is  essentially  the  same  in  diameter  as 
atD'. 

4Diameter  at  D  is  20#  greater  than  at  D". 

5 Bucket  of  of  high  speed  runner  has  parallel  edges  but  is  cut  back  as  shown  in  B. 

141.  The  Details  of  the  Runner. — The  reaction  runner  will  vary 
in  design  with  the  conditions  under  which  it  is  to  operate  and  the 
experience  and  ideas  of  its  designer.  In  American  practice  the 


Details  of  the  Runner. 


287 


manufacturer  usually  constructs  a  series  of  runners  of  similar  ho- 
mogeneous design ;  that  is  to  say,  each  wheel  of  the  series  has  all 
of  its  dimensions  proportional  to  that  of  every  other  wheel  of  the 
series,  and  is  of  similar  design  in  all  of  its  parts. 

On  account  of  demands  for  considerable  variations  in  speed  or 
power,  or  on  account  of  improvements  which  have  been  found  de- 
sirable by  reason  of  the  demands  of  his  trade,  the  manufacturer 
often  designs  and  constructs  several  series  of  wheels,  each  of  which 
is  particularly  adaptable  to  certain  conditions  which  he  has  had  to 
meet.  (See  Tables  XXII  and  XXIV.)  In  such  cases  each  series 
is  best  suited  for  the  particular  condition  for  which  it  was  designed, 
and  is  not  necessarily  obsolete  or  superseded  by  the  later  series. 


Fig.  174. 

The  curves  of  the  runner  buckets  (see  Figs.  13,  14,  133,  134,  136, 
146-148,  175)  must  be  such  as  to  receive  the  jet  of  water  from  the 
nozzle  or  guides  without  shock,  permit  it  to  pass  along  the  surface 
of  the  buckets  or  through  the  passages  in  the  runner  with  mini- 
mum friction,  and  discharge  it  as  nearly  devoid  of  velocity  as  prac- 
ticable. 

To  accomplish  this,  the  relative  position  and  relation  of  the 
curves  of  guides  and  buckets  must  be  carefully  arranged.  As  the 
jet  of  water,  is  always  directed  forward  in  the  direction  of  the  revo- 
lution of  the  wheel,  the  jet  has  an  original  velocity  in  that  direc- 
tion, and,  since  the  bucket  must  be  so  shaped  as  to  give  a  continued 
contact,  as  the  jet  progresses  and  the  wheel  revolves,  the  portion  of 
the  bucket  farthest  away  from  the  guides  must  be  curved  back- 
ward, and  terminate  at  such  an  angle  as  shall  permit  the  jet  to 
pass  away  from  the  wheel  with  free  discharge.  (See  Figs.  175  and 
128.) 


283  Turbine  Details  and  Appurtenances. 


B 


Fig.  175.— Curves  of  Buckets  and  Guides  in  Turbine  Wheels. 


Vertical  Turbine  Bearings. 


289 


RIGHT  HAND 


HAND 


Reaction  runners  are  made  either  right  or  left  handed  as  de- 
sired. When  looking  at  the  top  of  the  runner,  if  the  wheel  is  de- 
signed to  move  in  the  direction  of  the  hands  of  a  watch,  it  is  called 
a  right  handed  wheel,  and  if  it  moves  in  the  other  direction,  it  is 
called  a  left  handed  wheel.  (See  Fig.  176.) 

The  buckets,  hub,  crown,  and  ring  of  the  reaction  runner  must 
be  of  sufficient  strength  to  receive  the  impact  or  pressure  of  the 
moving  column  of  water  under  the  working  head,  and  to  transmit 
the  energy  to  the  shaft  through  which  it  is  to  be  transmitted  to  the 
machinery  to  be  operated. 

A  heavy  ring  is  usually  desirable,  both  to  give  strength  and 
support  to  the  outer  edge  of  the  buckets  and  also,  under  some  cir- 
cumstances, to  give  the  effect  of 
a  fly-wheel  in  order  to  materially 
assist  in  maintaining  uniform 
speed.  Floating  blocks  or  other 
material,  in  spite  of  the  use  of 
trash  racks,  sometimes  reach  the 
turbine,  and  when  caught  between 
the  buckets  and  the  case  are  apt 
Pig.  176.— "Hand"  of  Water  Wheels.  to  cause  serious  injury  to  the 

buckets. 

The  runner  is  attached  to  a  shaft  passing  through  the  hub,  to 
which  it  should  be  closely  fitted  and  strongly  keyed  to  prevent  its 
becoming  loosened  by  vibration  and  the  strain  of  operation.  This 
is^  especially  necessary  in  vertical  wheels,  for  if,  under  these  con- 
ditions, the  wheel  becomes  loosened  and  drops  from  the  shaft,  it  is 
apt  to  be  practically  destroyed.  Impulse  runners  acting  under  high 
heads  are  subject  to  heavy  shocks  and  must  be  especially  sub- 
stantial. 

142.  Vertical  Turbine  Bearings. — In  all  turbines  where  the  dis- 
charge is  axial  and  only  in  one  direction,  there  is  a  reaction  in  the 
other  direction  that  tends  to  unbalance  the  wheel  and  to  cause  a 
thrust  in  the  direction  opposite  to  the  discharge.  The  leakage  into 
the  space  back  of  the  runner  frequently  produces  a  thrust  in  the 
opposite  direction  which  may  be  wholly  or  partially  relieved  by 
openings  left  in  the  runner,  usually  close  to  the  axis.  In  large 
units  an  attempt  is  made  to  balance  these  various  pressures  with 
some  form  of  thrust  bearing  to  sustain  the  difference  in  pressure 
which  will  occur  under  different  conditions  of  operation. 


290 


Turbine  Details  and  Appurtenances. 


In  most  single  vertical  turbines  a  simple  step  bearing  is  used. 
The  bearing  itself  in  American  turbines  usually  consists  of  a  lig- 
num vitae  block,  turned  to  shape,  and  centered  in  a  bearing  block 
which  is  held  firmly  and  centrally  in  place  by  the  cross  trees.  The 
bearing  block  is  shown  by  T,  and  the  cross  trees  by  t,  in  Figs.  146, 
147  and  185.  The  bearing  on  the  shaft"  itself  is  usually  a  spherical 
sector,  or  some  other  symmetrical  curve  of  similar  form.  In  some 
cases  this  bearing  is  cut  directly  in  the  shaft  itself.  (See  Fig.  147.) 
In  others,  a  cast  iron  shoe  is  provided  and  attached  to  the  shaft. 
(See  M,  Figs.  145  and  184.)  Above  the  turbine  a  second  bearing 
is  also  provided  (see  T',  Figs.  145  and  147)  to  keep  the  shaft  in 
vertical  alignment.  This  bearing  in  American  wheels  is  usually 


Fig.  177. — Geylin   (Patent)    Glass  Suspension  Bearing   (R.  D.  Wood  &  Co.). 

of  the  type  shown  in  Fig..  182,  except  that  it  is  adapted  to  its  ver- 
tical position. 

In  the  Geylin-Jonval  turbine,  manufactured  by  R.  D.  Wood 
Company,  a  patent  glass  suspension  bearing  is  used.  (Fig.  177.) 
This  bearing  is  attached  above  the  wheel  (see  T,  Fig.  135)  and  has 
the  advantage  of  being  readily  accessible.  The  turbine  is  here  sus- 
pended on  a  circular  disc  composed  of  segments  of  glass,  B.  B. 
Fig.  177,  arranged  with  depressed  divisions  which  form  a  continu- 
ous space  around  each  segment  of  which  the  disc  is  composed,  al- 
lowing, while  the  turbine  is  in  motion,  a  perfect,  free  circulation 
of  the  lubricating  matter  with  which  the  space  is  filled.*  The  bear- 
ing is  a  true  metallic  ring,  A,  firmly  secured  to  the  turbine  shaft 
which  revolves  on  these  stationary  glass  segments. 

In  most  European  vertical  turbines  the  step  bearing  is  simply  a 
guide,  the  main  bearing  being  above  the  turbine  and  more  readily 
accessible  than  in  the  American  form. 


*  Catalogue  of  R.  D.  Wood  &  Co.,  1901,  p.  107. 


Vertical  Turbine  Bearings. 


291 


Figs.  178  and  179  represent  vertical  bearings  of  this  kind.  In 
these  bearings  C  is  a  spherical  sector  so  arranged  as  to  take  up  any 
slight  error  in  the  vertical  alignment  of  the  shaft.  Fig.  178  is  a 

ball  bearing;  the  hardened 
steel  balls,  AA,  revolve 
between  the  special  bear- 
ing plate,  B  and  Bi. 

In  Fig.  179  oil  is  pumped 
under  pressure  through  the 
inlet,  pipe  OE,  into  the 
space  A.  By  its  pressure 
the  bearing  plate,  B,  is 
raised  from  its  companion 
plate,  B,  and  the  oil  es- 
caping between  the  plates 
lubricates  them  and  over- 
flows through  the  overflow 
pipe,  OO. 

In  both  Figs.  178  and 
179  the  height  of  the  shaft 
is  adjusted  by  the  nut,'  N, 
which,  after  adjustment,  is 
fastened  securely  in  such 
position. 

At  the  power  plant  of 
The  Niagara  Falls  Power 
Company  a  thrust  or  hang- 
ing bearing  of  this  disc 
type,  somewhat  similar  to 
Fig.  179,  is  used  (See  Fig. 
180).  In  this  bearing  the 
shaft  is  suspended  to  a 
revolving  disc  carried  on 
a  stationary  disc.  The 

Fig   178.— Vertical    Suspension   Ball   Bear-      discs  are  of  close-grained 

ing.*  charcoal    iron    of  25,000 

pounds    tensile   strength 

and  of  14"  inside,  34"  outside  diameter.     The  lower  or  fixed  disk  is 
dowelled  to  a  third  disk  with  a  spherical  (3'  4"  radius)  seat.     This 


*Wasserkraftmaschinen  von  L.  Quantz. 


292 


Turbine  Details  and  Appurtenances. 


is  to  provide  for  an  automatic  adjustment  for  slight  deviations  from 
the  vertical  due  to  uneven  wear  of  the  discs  and  other  causes. 

The  bearing  surfaces  between  the  discs  are  grooved  to  allow  a 
circulation  and  distribution  of  the  oil  over  the  surface. 

Three  methods  of  lubri- 
cation, —forced,  self,  and 
a  combination  system, 
were  experimented  with 
and  the  combination  sys- 
tem finally  adopted.  In 
the  system  of  forced  lub- 
rication, the  oil  enters  the 
fixed  disc  at  two  diamet- 
rically opposite  points  and 
is  forced  between  the  discs 
under  400  pounds  pres- 
sure. Self-lubrication  is 
accomplished  by  oil  sup- 
plied at  the  inner  circum- 
ference of  the  disc  and 
thrown  outward  by  cen- 
trifugal force. 

The    disc    bearings     are 

enclosed  in  a  case  provided  with  sight  holes  through  which  the 
condition  of  the  bearing  as  well  as  the  temperature  of  the  oil  can 
be  observed.  A  thermometer  and  an  incandescent  light  are  sus- 
pended in  the  casing  for  this  purpose.  The  oil  is  cooled  by  water 
circulating  pipes  inside  the  casing. 

The  shaft  is  provided  with  a  balancing  piston  (see  Fig.  181) 
supplied  with  water  from  a  pipe  entirely  independent  of  the  pen- 
stock and  under  a  head  of  136  feet.  This  piston  carries  the  greater 
part  of  the  load,  less  than  2  per  cent,  of  the  load  being  left  to  be 
carried  by  the  oil-lubricated  disc  bearing  described  above. 

143.  Horizontal  Turbine  Bearings. — In  horizontal  wheels  vari- 
ous forms  of  bearing  may  be  used  according  to  the  conditions  and 
circumstances  of  their  operation.  When  practicable  the  bearings 
should  not  be  submerged  and  should  otherwise  be  made  as  accessi- 
ble as  possible.  In  such  cases  the  forms  of  bearings  may  be  the 
same  as  those  used  on  other  machines  subject  to  similar  strains. 


Fig. 


179. — Vertical    Suspension 
sure   Bearing.* 


Pres- 


*  Wasserkraftmaschinen  von  L.  Quantz. 


Horizontal  Turbine   Bearings. 


293 


In  many  horizontal  American  wheels,  where  submerged  bearings 
are  necessary,  lignum  vitae  bearings  are  used  similar  in  type  to  the 
upper  vertical  bearing  before  mentioned  (see  T',  Figs.  145  and  147). 
Such  a  bearing  is  shown  in  detail  in  Fig.  182.  In  this  bearing  the 
shaft,  S,  is  sustained  in  position  by  the  blocks,  TT,  which  fit  the 


For  Elecfr*. 
V/ires 


Thrust  Girder 
Section  through  Ball  Disk  Oil  Inlet 


OH  Catcher 
Section  through  Oil  Sight  Hole. 


Fig.   180.— Vertical   Thrust   or   Hanging  Bearing  of   the   Ni- 
agara Falls  Power  Co.   (See  Eng.  Record,  Nov.  28, 1903.) 

recesses  of  the  cast  iron  bearing  block,  K,  which  in  turn  is  attached 
to  a  cross  tie  in  the  case  or  to  a  pedestal,  P.  The  blocks,  TT,  are 
adjusted  by  means  of  the  screws,  BB,  which,  after  adjustment 
are  locked  in  position  by  the  lock  nuts,  LL.  Such  submerged 
bearings  are  sometimes  lubricated  by  water  only,  in  which  case  op- 


294 


Turbine  Details  and  Appurtenances. 


portunity  must  be  given  for  the  free  circulation  of  the  water.  In 
other  cases  the  boxes  are  made  tight  and  flow  into  them  along  the 
shaft  is  prevented  by  stuffing  boxes  at  each  end  of  the  main  box, 

the  boxes  being  lubricated 
by  forced  , grease  lubrica- 
tion. 

Bronze  boxes  of  the  types 
used  for  other  high  grade 
machines  are  sometimes 
used  for  submerged  bear- 
ings. In  such  cases  great 
care  is  necessary  to  pre- 
vent the  entrance  of  grit- 
bearing  waters.  Such 
bearings  are  lubricated  by 
forced  oil  or. grease. 

In  forced  lubrication  it 
is  desirable  that  both  a 
force  and  return  pipe  be 
used  so  as  to  give  visible 
evidence  that-  the  lubri- 
cant is  actually  reaching 
the  bearing.  In  some 


Fig.  181. — Section  of  Turbine  used  in  new 
Power  House  of  The  Niagara  Falls  Power 
Company,  showing  Balancing  Hydraulic 
Position  used  to  sustain  Turbine  and  Shaft. 
(Eng.  Record,  Nov.  28,  1903.) 


cases  bearings  that  would 
be  otherwise  submerged 
are  made  accessible  at  all 
times  by  metallic  tubes 
(see  Fig.  322)  used  as 
manholes. 

Where  the  turbine  is  placed  horizontally,  gravity  can  no  longer 
offset  the  thrust  caused  by  the  reaction  of  the  turbine  when  the 
discharge  is  in  one  direction,  and  the  thrust  must  therefore  be  over- 
come by  the  use  of  some  form  of  thrust-bearing.  Where  other  con- 
ditions permit,  it  is  quite  common  practice  to  install  two  turbines 
on  a  single  horizontal  shaft,  having  their  discharges  in  opposite  di- 
rections, in  which  case  the  thrust  of  each  turbine  is  overcome  by 
the  thrust  of  its  companion  (see  Figs.  153,  160  and  316).  In  many 
cases,  however,  the  arrangement,  size  and  capacity  of  the  wheels 
to  be  used  are  not  such  as  will  permit  the  use  of  twin  turbines  and 
thrust-bearing,  and  other  means  of  taking  up  the  thrust  must  be 
provided. 


Horizontal  Turbine   Bearings. 


295 


144.  Thrust-Bearing  in  Snoqualmie  Falls  Turbine. — In  the  Sno 
qualmie  Falls  Turbine,  manufactured  by  The  Platt  Iron  Works 
Company  (see  Figs.  161  and  162),  the  device  for  taking  up  the 
thrust  is  thus  described  by  the  designing  engineer,  Mr.  A.  Giesler:* 

"Single-wheel  horizontal-shaft  units  are  relatively  infrequent  in 
turbine  practice,  especially  in  large  sizes,  where  the  thrust  of  a  sin- 
gle runner  is  large  enough  to  require  careful  consideration.  The 
thrust  is  made  of  two  parts :  (I)  that  due  to  the  static  pressure  or 
effective  head  of  water  at  the  various  points  of  the  runner  surface ; 
.and  (2)  that  due  to  the  deflection  of  the  water  from  a  purely  radial 


B 


Fig.  182. — Horizontal-  Lignum  Vitae  Bearing  as  Used  in  American  Turbines. 

path  through  the  wheel.  As  concerns  the  first  part,  the  front  face 
of  the  wheel  is  pressed  upon  by  a  pressure  varying  from  the  supply 
head  at  the  outer  circumference  to  the  discharge  pressure  (vacuum) 
at  the  inner  edge  of  the  vanes,  which  latter  extends  over  the  whole 
central  area  of  the  runner  (and  shaft  extension).  The  rear  face  of 
the  runner  is  subjected  to  the  pressure  of  water  leaking  through 
the  radial  air-gap  between  casing  and  runner,  substantially  equal  to 
the  supply  head.  This  greatly  overbalances  the  pressure  on  the 
front  face,  and  the  resultant  thrust  is\to  the  right  in  Fig.  161  (to- 
ward the  draft  tube).  The.  discharge  ends  of  the  vanes,  being 
:urved  transversely,  also  havfe  a  pressure  component  directed  to- 


*  See  "Engineering  News"  of  March  29,  1906. 


296 


Turbine  Details  and  Appurtenances. 


ward  the  right.  The  velocity  effect  produces  a  thrust  directed  to- 
ward the  left,  but  this  is  very  small  and  does  not  materially  reduce 
the  pressure  thrust. 

"By  far  the  larger  part  of  the  pressure  thrust  is  eliminated  by 
venting  the  space  back  of  the  runner  into  the  discharge  space.  Six 
holes  through  the  wheel  near  the  shaft,  indicated  in  Fig.  161,  have 
this  function.  The  water  leaking  in  through  the  air-gap  is  continu- 
ously discharged  through  these  vents  into  the  draft-tube,  and  the 
accumulation  of  any  large  static  pressure  back  of  the  wheel  is 
thereby  avoided. 

"The  average  pressure  on  the  front  of  the  runner,  however,  is 
always  lower,  and  the  resultant  thrust  is  therefore  toward  the  draft- 


f *¥- •*• 


Cross     Section.  Longitudinal     Section* 

Fig.  183. — Thrust-Bearing  Snoqualmie  Wheels. 

tube,  though  its  amount  varies  considerably,  being  greatest  for  full 
gate  opening.  This  thrust  is  taken  up  by  the  balancing  piston  im- 
mediately back  of  the  rear  head  of  the  wheel  case,  and  the  ultimate 
balance  and  adjustment  of  position  is  accomplished  by  the  collar 
thrust-bearing  behind  the  balancing  piston. 

"The  balancing  piston  is  a  forged  enlargement  of  the  shaft,  fin- 
ished to  a  diameter  of  17  inches,  which  works  in  a  brass  sleeve  set 
in  a  hub-like  projection  on  the  back  of  the  wheel-housing.  The  in- 
side of  the  sleeve  has  six  circumferential  grooves,  each  one  inch  wide 
and  one-quarter  inch  deep,  as  water  packing.  The  chamber  in  front 
of  the  piston  communicates  by  a  pipe  (containing  a  strainer)  with 
the  supply  casing  of  the  water-wheel,  and  therefore  receives  the 
full  pressure  of  the  supply  head.  The  chamber  back  of  the  piston 


Thrust-Bearing  in  Snoqualmie  Falls  Turbine.  297 

is  drained  to  the  draft-tube,  so  as  to  carry  off  any  leakage  past  the 
piston.  The  device  thus  produces  a  constant  thrust  on  the  piston, 
directed  toward  the  left.  By  throttling  the  pressure  pipe  this 
thrust  can  be  adjusted  as  desired. 

"The  thrust-bearing  shown  in  Fig.  161  and  in  detail  in  Fig.  183 
consists  of  a  group  of  four  collars  on  the  shaft,  working  in  a  babbit- 
ted thrust-block  which  is  bolted  to  the  back  of  the  wheel-housing. 
The  collars  are  formed  on  a  steel  sleeve  which  fits  over  the  shaft 
and  is  bolted  to  the  rear  face  of  the  balancing  piston ;  this  makes 
it  possible,  when  the  collars  are  worn  out,  to  renew  the  bearing  by 
dismounting  the  thrust-block  and  placing  a  new  sleeve.  The 
thrust-bearing  is  lubricated  by  oil  immersion.  An  oil  chamber  is 
cored  in  the  block  and  communicates  by  numerous  oil  holes  with 
the  bearing  faces ;  a  constant  flow  of  oil  is  maintained  by  means  of 
oil-supply  and  drain-pipes.  Concentric  with  the  oil  chamber  and 
outside  of  it  a  water  chamber  is  cored  in  the  block.  Cooling  water 
is  supplied  to  this  chamber  by  a  pipe  from  the  pressure  side  of  the 
turbine,  and  drains  from  the  top  of  the  bearing  through  a  drain-pipe 
to  the  draft-tube.  A  U-pipe  attached  at  one  side  of  the  bearing  forms 
connection  between  the  water  chambers  of  the  upper  and  lower 
halves  of  the  block.  This  detail  avoids  making  the  connection  by  a 
hole  through  the  joint  face,  which  would  allow  leakage  of  water 
into  the  oil-space  and  into  the  bearing. 

"The  balancing  piston  is  so  proportioned  and  the  pressure  supply 
pipe  is  throttled  to  such  a  point  as  to  give  exact  balance  (i.  e.,  with 
zero  thrust  in  the  thrust-bearing)  at  about  half  to  five-eighths  the 
full  output  of  the  wheel.  At  larger  power  there  will  be  an  unbal- 
anced thrust  to  the  right,  and  at  smaller  output  to  the  left,  which 
are  taken  by  the  thrust-bearings.  The  maximum  thrust  on  the 
collars  is  about  25,000  Ibs.  The  collars  are  2i/2  inches  high  (2% 
.inches  effective)  by  131/2  inches  mean  diameter,  giving  a  total  effec- 
tive bearing  area  on  four  collars  of  418  sq.  inches.  The  maximum 
collar  pressure  is  thus  about  60  Ibs.  per  sq.  in." 

145.  The  Chute  Case.— The  chute  case  (see  Figs.  146,  147  and  .184) 
consists  of  the  fixed  portion  of  the  turbine  to  which  are  attached 
the  step  and  bearings  of  the  wheel  (T),  the  guide  passages  (g) 
which  direct  the  passage  of  the  water  into  the  turbine  bucket,  and 
the  gates  (G)  which  control  the  entrance  of  the  water,  and  also 
the  case  cover  (C).  The  case  cover  keeps  the  wheel  from  contact 
18 


298 


Turbine  Details  and  Appurtenances. 


with  the  water  except  as  it  passes  through  the  guide  and  gates.  To 
the  chute  case  is  usually  attached  the  apparatus  and  mechanism  for 
manipulating  or  controlling  the  position  and  opening  of  the  gate. 
(A.  P,  Gr.,  etc.)  In  vertical  turbines  a  tube,  d,  is  usually  attached 
to  the  lower  ring,  forming  a  casing  in  which  the  lower  portion  of 
the  turbine  revolves  and  on  which  the  bridge  tree,  t,  holding  the 

step  bearing  is  attached. 
When  this  tube  is  no  long- 
er than  one  diameter  it  is 
usually  called  the  turbine 
tube;  but  when  it  is  con- 
siderably extended,  it  is 
termed  a  draft  tube. 

The  design  of  the  tur- 
bine tube  depends  largely 
on  the  character  of  the 
wheel.  Some  wheels  dis- 
charge downward  and  in- 
ward, some  almost  entire- 
ly downward,  some  down- 
ward and  outward,  and  in 
some  cases,  the  wheel  dis- 
charges in  all  three  direc- 
tions. For  the  best  re- 
sults the  tube  should  be 
so  designed  that  the  water 
from  the  wheel  shall  be 
received  by  it  with  no 
radical  change  of  velocity 
and  so  that  the  remaining 
velocity  will  be  gradually 
reduced  and  the  water 
discharged  at  the  lowest 
practicable  velocity. 

The  chute  case  and  its  appurtenances  should  be  so  designed  that 
the  water  will  enter  the  bucket  with  the  least  possible  shock  or  re- 
sistance at  all  stages  of  gate  and  with  a  gradual  change  in  velocity, 
and  will  discharge  from  the  buckets  into  the  turbine  tube  with  as 
little  eddying  as  possible  and  be  evenly  distributed  over  the  cross 
section  of  the  tube  so  as  to  utilize  the  suction  action  of  an  unbroken 
column  of  water.  The  case  must  also  be  designed  of  sufficient 


Fis.  184. 


The  Chute  Case. 


299 


Fig.  185.— Section  Swain  Turbine. 


strength  to  sustain  the  weight  of  the  turbine  wheel  and  so  that  the 
step  bearings  are  accessible  and  can  be  readily  replaced  or  adjusted. 
The  arrangement  of  the  case  must  also  be  such  that  the  openings 
between  the  wheel  and  the  case  are  as  small  as  practicable  and  the 

line  of  possible  leakage 
will  be  as  indirect  as  pos- 
sible so  as  to  avoid  leak- 
age loss. 

Most  chute  cases  are 
either  cast  or  wrought 
iron.  Cast  iron  usually 
lends  itself  to  a  more  sat- 
isfactory design  for  receiv- 
ing and  passing*  the  water 
without  sudden  enlarge- 
ment and  opportunities 
for  losses  by  sharp  angles 
and  irregular  passageways. 
Wrought  iron,  while  not 
always  lending  itself  read- 
ily to  designs  which  elim- 
inate all  such  losses,  possesses  much  greater  strength  for  a  given 
weight  which  is  a  great  advantage  under  some  conditions. 

146.  Turbine  Gates. — Three  forms  of  gates  are  in  common  use 
for  controlling  the  admission  of  water  into  reaction  turbines.  The 
cylinder  gate  consists  of  a  cylinder  closely  fitting  the  guide  that 
by  its  position  admits  or  restricts  the  flow  of  water  into  the  buck- 
ets. Fig.  184  is  a  section  of  a  turbine  of  the  McCormick  type, 
manufactured  by  the  Wellman-Seaver-Morgan  Company,  having 
a  gate  of  this  type,  GG,  between  the  guides  and  runners,  which  is 
shown  closed  in  the  cut.  The  gate  is  operated  by  the  gearing,  Gr., 
which  raises  it  into  the  dome,  O,  through  connection  with  the  gov- 
ernor shaft,  P.  This  same  type  of  gate  is  used  over  the  discharge 
of  the  Niagara- Fourneyron  turbine  (see  GG,  Fig.  134),  over  the 
inlet  of  the  Geylin-Jonval  turbine,  GG,  Figs.  135  and  137,  and  be- 
tween the  guides  and  buckets  of  the  Niagara  turbine,  shown  in 
Fig.  101. 

A  modified  form  of  the  cylinder  gate  is  that  used  by  the  Swain 
'Turbine  Company  (see  Fig.  185),  which  is  lowered  instead  of  being 
raised  into  the  dome  as  in  Fig.  184. 


3°° 


Turbine  Details  and  Appurtenances. 


A  similar  modification,  called  a  sleeve  gate  by  its  designer,  J.  W. 
Taylor,  is  shown  in  Fig.  186. 

When  partially  closed  the  cylinder  gate  causes  a  sudden  contrac- 
tion in  the  vein  of  water  which  is  again  suddenly  enlarged  in  enter- 
ing the  runner  after  opening  the  gate.  (See  Fig.  188.)  These  con- 
ditions produce  eddying  which  results  in  decreased  efficiency  at 
part  gate.  (See  Figs.  185  and  186.) 

The  wicket  gate,  when  well 
made,  is  perhaps  the  most  satisfac- 
tory gate,  especially  for  moderate 
or  high  heads.  It  can  be  readily 
balanced  and  should  be  made  with 
perhaps  a  tendency  to  drift  shut, 
so  that  should  the  governor  mech- 
anism break  or  become  disabled, 
the  gates  will  drift  shut.  These 
gates  are  illustrated  by  GG, 
Figs.  147  and  148,  which  illustrate 
the  wicket  gate  of  the  Samson 
turbine  of  The  James  Leffel  & 
Company,  and  Fig.  187  which 
shows  the  wicket  gate  of  the  Well- 
man-Seaver-Morgan  Company. 
In  both  cases  the  wickets  are  con- 
nected by  rods  with  the  eccentric 
circle  and  through  an  arm  and 
section  with  the  gearing  Gr. 

Figs.  145  and  146  show  the  wick- 
et gate    of    the    Improved    New 
American,  and  Figs.  161   and   162 
show  the  wicket  gates  of  the  Sno- 
qualmie  Falls   turbine,    manufact- 
ured   by   The    Platt    Iron  Works.  - 
In  both  the  New  American    and 
Fig.     186.— Section     Taylor     Sleeve  Snoqualmie  wheels,  the  gates  are 
Gate-  moved    by  a   gate    ring    (see   Gr. 

Fig.  145).     Figs.  189  and  190  show 

the  details  of  the  wicket  gates  and  connection  of  the  same  to  the 
gate  ring  of  the  Snoqualmie  Falls  Turbine. 

The  tendency  to  produce  eddying  is  much  reduced  in  well  de- 
signed wicket  gates,  although  the  sudden  enlargement  of  the  re- 


Turbine  Gates. 


301 


duced  vein  at  part  gate  undoubtedly  reduces  the  efficiency  of  the 
wheel.  (See  Fig.  191,  A  and  B.) 

The  register  gate  (see  G,  Fig.  192)  consists  of  a  cylinder  case 
with  apertures  to  correspond  with  the  apertures  in  the  guides,  g, 
and  is  so  arranged  that,  when  in  proper  position,  the  apertures  reg- 
ister and  freely  admit  the  water  to  the  wheel,  and  is  also  so  con- 
structed that  when  properly  turned  the  gate  cuts  off  the  passage 
completely  or  partially  as  desired. 

Considerable  eddying  is  produced  by  the  partially  closed  reg- 
ister gate,  with  a  consequent  decrease  in  part  gate  efficiency.  (See 

Fig.  193.)  The  cylinder 
gate  is  usually  the  cheapest 
and  most  simple  form  of 
gate,  but  the  wicket  gate, 
if  properly  designed  and 
constructed  seems  to  ad- 
mit of  the  entrance  of 
water  into  the  bucket  with 
least  possible  resistance 
and  eddying,  and  in  the 
most  efficient  manner. 
This  form  of  gate  is  the 
most  widely  used  in  high- 
grade  turbine  construc- 
tion at  the  present  time, 
although  the  cylinder  gate 
is 'largely  in  use  and  has 
given  satisfactory  results. 
In  some  cases  the  pas- 
sage of  water  is  restricted 
or  throttled  by  the  use  of 

a  butterfly  valve,  either  in  the  inlet  or  in  the  turbine  tube.  This 
throttles  the  inlet  or  discharge  and  regulates  the  head  in  a  very 
inefficient  manner,  but  may  be  reasonably  satisfactory  where  econ- 
omy of  water  is  unnecessary. 

In  impulse  wheels  the  gates  are  usually  so  arranged  that  the 
guide  passages  are  opened  one  at  a  time  instead  of  all  opening  par- 
tially, as  in  part  gate  conditions  with  the  reaction  wheel.  This  re- 
sults in  less  loss  in  the  eddyings  caused  by  part  gate.  Fig.  194 
shows  the  type  of  gate  used  by  The  Platt  Iron  Works  in  their  Gir- 


Fig. 


187.— Wicket   Gate    of   the   Wellman- 
Seaver  Morgan  Co. 


302 


Turbine  Details  and  Appurtenances. 


ard  turbines  where  the  guide  passages  are  arranged  symmetrically 
in  three  groups  about  the  wheel.  In  the  tangential  wheel,  where 
a  single  nozzle  is  used,  the  most  efficient  method  found  for  redu- 
cing the  opening  is  with  the  needle  as  illustrated  in  Fig.  195.  This 
figure  shows  a  cross  section  of  +he  Doble  needle  nozzle,  a  form 
which  gives  a  high  velocity  coefficient  under  a  very  wide  range  of 
opening.  The  character  of  the  stream  from  a  needle  nozzle  when 

greatly  reduced  is  shown  by  Fig. 
196  where  the  clear  and  solid 
stream  gives  evidence  of  high  effi- 
ciency. If  the  flow  of  water 
through  the  nozzle  is  regulated  by 
throttling  the  water  with  a  valve 
before  it  reaches  the  nozzle,  a 
very  low  efficiency  results. 

147.  The  Draft  Tube.— The  re- 
action wheel  is  of  particular  ad- 
vantage under  low  heads  on  ac- 
count of  the  fact  that  it  can  run 
efficiently  under  water,  and  there- 
fore, under  backwater  conditions, 
can  be  made  to  utilize  the  full  head 
available.  It  is  not  necessary, 
however,  to  set  the  reaction  wheel 
low  enough  so  that  it  will  be  below 
water  at  all  times  for  the  principle 
of  the  suction  pipe  can  be  utilized 
and  the  wheel  set  at  any  reason- 
able ^distance  above  the  tail  water 
and  connected  thereto  by  a  draft 
tube  which,  if  properly  arranged, 

will  permit  the  utilization  of  the  full  head  by  action  of  the  draft 
or  suction  pull  exerted  on  the*  wheel  by  the  water  leaving  the 
turbine  through  the  tube  from  which  all  air  has  been  exhausted. 
The  water  issuing  from  the  turbine  into  a  draft  tube,  which  at  the 
starting  is  full  of  air,  takes  up  the  air  in  passing  and  soon  estab- 
lishes the  vacuum  necessary  for  the  draft  tube  effects.  The  func- 
tion of  the  draft  tube  is  not  only  to  enable  the  turbine  to  utilize 
by  suction  that  part  of  the  fall  from  the  wheel  discharge  to  the  tail 
water  level,  but  it  should  also  gradually  increase  in  diameter  so  as 


Fig.  188. — Showing  Cylinder  Gate 
Partially  Open  and  Eddies  Caused 
by  Sudden  Contraction  and  En- 
largement of  Entering  Vein  of 
Water. 


Turbine  Gates. 


303 


Section    A-B. 


;£-*^jf 

it**?3-* 


Fig.   189. — Showing  Relations  of  Gate  Guides  and   Buckets    in   Snoqualmie 
Falls  Turbine  (Platt  Iron  Works  Co.). 


Gate  Arm 


Cover  Ring  •*£_ 


f/r^/%^ 

'&zfe  Operating 
Ring 

^§<§&/%yy2r     ' 

w  fro.m  Governor  Ar/n> 

''•Operating  Pin  oj  2  Operating  Pin  Brackets1 
"       •    •    '  Screwd  to  Gate  Operating 
ffing;  I80°apart, 

Section    A-B. 
^ 

Fig.  190.— Showing  Rigging  for  the  Operation  of  Wicket  Gate  in  Snoqualmie 
Falls  Turbine  (Platt  Iron  Works  Co.). 


304 


Turbine  Details  and  Appurtenances. 


A.     Gate  wide  open.  B.     Partial  gate. 

Fig.  191. — Showing  Condition  of  Flow  Through  Open  and  Partially  Closed 

Wicket  Gates. 


to  gradually  decrease  the 
velocity  of  the  water  after 
it  is  discharged  from  the 
turbine  wheel,  thus  enab- 
ling the  turbine  to  utilize 
as  much  as  possible  of  the 
velocity  head  with  which 
the  water  leaves  the  tur- 
bine. It  should  be  noted 
that  a  partial  vacuum  is 
established  in  the  draft 
tube  and,  therefore,  the 
draft  tube  must  be  strong 
enough  to  stand  the  exte 
rior  pressure  due  to  the 
vacuum  so  created.  In  or- 
der to  perform  its  functions 
Iron  ..  ,.  e 

in  a  more  satisfactory  man- 
ner, it  must  also  be  made 
perfectly  air  tight. 

One  of  the  great  advantages  in  the  use  of  the  draft  tube  is  the 
possibility,  by  its  use,  of  setting  the  wheel  at  such  an  elevation 


Fig. 


192.— Register     Gate 
Works   Co.). 


(Platt 


Turbine  Gates. 


305 


above  the  tail  water  that  the  wheel  and  its  parts  can  be  properly 
inspected,  by  draining  the  water  from  the  wheel  pit.  Otherwise  it 
would  be  necessary  to  install  gates  in  the  tail  race  and  pumps  for 
pumping  out  the  pit  in  order  to  make  the  wheel  accessible.  The- 
oretically, the  draft  tube  can  be  used  of  as  great  length  as  the  suc- 
tion pipe  of  a  pump,  and  this  is  probably  true  of  draft  tubes  for 

very  small  wheels.  Practically,  the 
draft  tube  should  seldom  be  as 
long  as  20  feet,  especially  for  large 
wheels,  for  its  success  in  the  util- 
ization of  the  head  depends  on  the 
maintenance  of  an  unbroken  col- 
umn of  solid  water,  which  is  diffi- 
cult to  maintain  in  large  tubes.  As 
the  size  of  the  wheel  increases  the 
difficulties  of  maintaining  a  vac- 
uum increase  and  the  length  of  the 
draft  tube  should  correspondingly 
decrease.  It  is  practically  impos- 
sible to  maintain  a  working  head 
with  large  turbines  through  long 
draft  tubes  with  the  turbine  set  at 
great  distances  above  the  water. 
Long  draft  tubes  should,  as  a  rule, 
be  avoided  and  in  all  cases  where 

I  ^jfij   |H    J^ draft  tubes  are  used,  they  should  be 

as  straight  and  direct  and  as  nearly 
vertical  as  possible.  It  is  the  prin- 
ciple of  the  draft  tube  that  per- 
mits horizontal  shaft  wheels  to  be 
utilized,  as  otherwise,  with  this 

type  of  machinery,  only  a  small  portion  of  the  head  could  be  used 
to  advantage  under  normal  conditions,  for  such  wheels  being  often 
direct  connected  to  the  machinery  are,  of  necessity,  placed  above 
the  tail  water.  The  draft  tube  is  commonly  of  iron  or  steel,  but  in 
plants  where  concrete  construction  is  used  the  draft  tube  may  be 
formed  directly  in  the  concrete  of  the  station  or  wheel  foundations. 
On  the  Fourneyron  turbine  Boyden  used  what  he  termed  a  diffu- 
ser.  (See  Fig.  197.)  The  main  purpose  of  the  diffuser,  and  of  the 
conical  tube  as  well,  is  to  furnish  a  gradually  enlarged  passage 
through  which  the  velocity  of  the  water  as  it  leaves  the  wheel  is 


Fig.  193.— Showing  Eddying  Caused 
by  Partial  Closure  of  Register 
Gate. 


306 


Turbine  Details  and  Appurtenances. 


Fig.  194. — Gates  and  Guides  of  Girard  Impulse  Turbine.  (Turbine  Design 
as  Modified  for  Close  Speed  Regulation,  G.  A.  Buvinger,  Proc.  Am,  Soc. 
M.  E.,  Vol.  XXVII.) 


Fig.  195. — Cross-section  of  Doble  Needle  Nozzle.* 


*  From  Bulletin  No.  6,  Abner  Doble  Co. 


The  Draft  Tube. 


307 


Fig.  196. — Stream  from  Doble  Needle  Nozzle.* 


so  gradually  reduced  as  to 
enable  the  velocity  head  to 
be  utilized  in  the  wheel, 
thus  saving  head  which 
would  otherwise  be  lost. 
It  has  already  been  noted 
that  impulse  wheels  of  the 
Pelton  and  Girard  types 
cannot  operate  satisfactor- 
ily submerged,  and  must 
be  set  at  such  positions 
that  they  will  be  above  the 
tail  water  at  all  times.  In 
many  localities  where  the 

Fig.  197.-Boyden  Diffuser.  variation  in  the  surface  of 

tail  waters  is  considerable, 

this  means  a  large  relative  loss  in  the  head  utilized  and  that  this 
type  of  wheel  will   therefore  not  be  practicable  except  under  high 

'    *  From  Bulletin  No    6,  Abner  Doble  Co. 


308  Turbine  Details  and  Appurtenances. 

head  conditions  and  where  the  loss  entailed  by  the  rise  and  fall  of 
the  tail  water  will  be  inconsiderable.  An  attempt  has  been  made, 
however,  to  so  design  a  draft  tube  that  a  vacuum  will  be  established 
and  maintained  below  the  wheel,  in  such  a  manner,  however,  that 
the  water  will  not  come  in  contact  with  the  wheel.  The  vacuum  is 
so  maintained  as  to  hold  the  water  at  an  established  point  just  below 
the  wheel,  thus  permitting  the  wheel  to  utilize  the  full  head  except 
for  the  small  clearance  between  the  wheel  and  the  water  surface  in 
the  draft  tube.  This  arrangement  is  shown  in  Figs.  168  and  171,  as 
applied  by  The  Platt  Iron  Works  Company  to  a  Girard  turbine. 


CHAPTER  XIV 

HYDRAULICS  OF  THE  TURBINE. 

148.  Practical  Hydraulics  of  the  Turbine. — It  is  not  the  purpose 
of  this  chapter  to  consider  mathematically  and  at  length  the  princi- 
ples of  hydraulic  flow  in  relation  to  the  curves  of  guides  and  buckets 
and  the  effects  of  such  curves  on  the  power  and  efficiency  of  the  tur- 
bine. These  relations  are  expressed  by  long  and  involved  equations 
of  considerable  interest  to  the  engineer  who  is  to  design  and  con- 
struct the  turbine  but  of  little  practical  value  to  the  engineer  who  is 
to  select  and  install  it  in  a  water  power  plant.  Few  of  the  designers 
of  American  wheels  have  given  much  attention  to  the  involved 
mathematics  of  hydraulic  flow  in  the  turbine  and  the  designs  of 
most  American  wheels  are  based  on  the  results  of  experiment  and 
broad  practical  experience.  The  designs  of  Swiss  and  German 
wheels  are,  to  a  much  greater  extent,  based  on  mathematical 
analysis.  It  is  an  open  question  whether  the  best  work  of  either 
American  or  foreign  manufacture  shows  any  marked  superiority 
in  comparison  with  the  other.  The  results  actually  attained  in  the 
manufacture  of  wheels  in  this  country  seem  to  show  that  the 
American  practice  in  wheel  design  will  give  equal  and  even  more 
uniformly  satisfactory  results  than  the  European  methods, — at 
least  as  carried  out  by  foreign  engineers  under  American  condi- 
tions. 

Correct  theory  must  be  the  basis  of  all  successful  work.  The 
theory  of  the  experienced  man  may  be  unformulated  and  unex- 
pressed, but  correct  design  has  always  a  correct  theory  as  its  basis 
even  if  unrecognized  as  such,  and  such  a  theory  properly  applied  will 
lead  to  correct  results.  On  the  other  hand,  formulated  theory  will 
lead  to  correct  results  only  as  far  as  the  theory  is  correct  and  takes 
into  account  all  controlling  or  modifying  factors  and  is  properly  ap- 
plied. A  correct  theory,  carefully  formulated  and  properly  applied, 
cannot  fail  to  be  of  great  service  to  the  engineer  in  extending  his 
experience  to  wider  fields.  Scientific  study  and  mathematical  an- 
alysis of  the  turbine,  based  on  wide  experience  and  careful  experi- 
ments, can  but  lead  to  the  accomplishment  of  better  results  than 
have  vet  been  attained. 


3io  Hydraulics  of  the  Turbine. 

An  understanding  of  certain  laws  of  flow  through  turbines  as  con- 
firmed by  both  theory  and  practice  is  essential  to  a  proper  compre- 
hension of  the  principles  which  should  govern  the  selection  and 
installation  of  such  wheels  and  these  laws  are  considered  in  this 
chapter. 

149.  Nomenclature  used  in  Chapter. — In  the  discussion  in  this 
chapter  the  letters  and  symbols  used  have  the  following  signifi- 
cance: 

a     —  Area  of  gate  orifice  or  orifices. 

a    —  Angle  of  deflection  of  jet. 

ft    =  Supplement  to  angle  of  deflection  =  180°  —  a.. 

D   =  Diameter  of  wheel  in  inches. 

E   =  Energy  in  foot  pounds  per  second. 

F    =  Force  producing  pressure  or  motion. 

g    =  Acceleration  of  gravity. 

h    =  Effective  head  at  the  wheel. 

n    =  Number  of  revolutions  per  minute. 

nj  =  Number  of  revolutions  per  minute  for  head  h^. 

it    —  Ratio  of  circumference  to  diameter  =  3.1416 

P    =  Horse  powers  of  turbine  at  any  given  head. 

P!  =  Horse  power  of  turbine  at  head  hj. 

q    =  Discharge  in  cubic  feet  per  second  at  any  given  head. 

q1  =  Discharge  in  cubic  feet  per  second  at  head  hx. 

rx  =  Internal  radius  of  wheel. 

r2  =  External  radius  of  wheel. 

S    =  Space  passed  through  by  force  acting. ; 

iij  —  Velocity  of  wheel  at  gate  entrance. 

u2  —  Velocity  of  wheel  at  point  of  discharge. 

v    =  Theoretical  spouting  velocity  due  to  head  = 

v'  =  Velocity  of  the  periphery  of  the  impeller,  in  feet  per  second. 

v,  =  Absolute  velocity  of  water  entering  the  wheel. 

v2  =  Absolute  velocity  of  water  leaving  the  wheel. 

vr  =  Relative  velocity  of  water  entering  the  wheel. 

VR  =  Relative  velocity  of  water  leaving  the  wheel. 

va  =  Average  velocity. 

W  —  Total  weight  per  second. 

w   =  Weight  of  unit  of  water  =  62.5  Ibs. 

cp  =  Ratio  peripheral  velocity  of  wheel  to  spouting  velocity  of  water  =  — 

TURBINE    CONSTANTS. 

C   =  Coefficient  of  discharge  of  gate  orifice  or  orifices. 

A  =  Constant  relation  of  turbine  diameter  and  speed. 

K   =  Constant  relation  of  turbine  diameter  to  discharge. 

K3  =  Constant  relation  of  turbine  diameter  to  power. 

Ka=  Constant  relation  of  peripheral  velocity. 

K4=  Coefficient  of  relation  of  turbine  speed  and  discharge. 

K6=  Coefficient  of  relation  of  turbine  power  and  speed.     (Specific  speed.) 


First  Principles.  311 

150.  First  Principles. — In  the  utilization  of  water  for  power  pur- 
poses it  is  the  first  principle  of  design  that  the  water  should  enter 
the  wheel  without  shock  and  leave  it  without  velocity.     This  should 
be  interpreted  to  mean  that  the  approaches  of  the  water  to  the  wheel 
must  be  such  as  to  cause  no  loss  by  undue  friction  or  by  sudden  con- 
tractions or  enlargements  (inducing  eddies  and  other  sources  of  lost 
energy),  and  that  all  shocks  should  be  confined  as  far  as  possible  to 
the  action  on  the  wheel  buckets  leaving  the  full  amount  of  energy, 
and  consequently  the  velocity,  to  be  entirely  converted  to  power 
therein. 

In  gravity  wheels,  illustrated  by  the  various  overshot  wheels  for- 
merly so  extensively  used  for  water  power  purposes,  the  water 
sho'tild  enter  the  wheel  at  the  lowest  practicable  velocity  and  should 
be  retained  in  the  buckets  until  the  buckets  have  made  the  greatest 
possible  descent  from  the  nearest  practicable  approach  to  the  eleva- 
tion of  head-water,  to  the  nearest  practicable  approach  to  the  eleva- 
tion of  the  tail  water.  Part  of  the  velocity  of  approach  to  the  wheel 
may  be  utilized  by  impact  on  the  buckets  but  the  entire  energy  re- 
maining in  the  water  as  it  falls  or  flows  away  from  the  wheel  is  lost, 
and  cannot  be  further  utilized  in  the  wheel. 

The  greater  the  reduction  in  velocity,  the  greater  the  proportion 
of  energy  that  can  be  utilized,  but  there  comes  a  limit  beyond  which 
it  is  not  practicable  to  go.  This  limit  varies  with  different  condi-> 
tions  and  may  be  the  result  of  too  great  expense  in  the  building  of 
raceways  or  in  the  construction  of  the  machine  itself.  A  point  will 
be  reached  where  the  friction  expended  in  the  large  machine  needed 
to  reduce  the  velocity  will  consume  more  energy  than  would  be  lost 
in  inducing  a  higher  velocity.  These  losses  must  be  equalized.  In 
practice  it  is  found  that  about  two  or  three  feet  per  second  are  satis- 
factory velocities  at  which  to  reject  or  discharge  the  water  used  by 
motors.  These  velocities  represent  heads  of  from  .062  to  ,14  feet, 
or  from  three-quarters  to  slightly  less  than  two  inches.  The  veloc- 
ity of  discharge  must,  however,  be  fixed  for  each  individual  case  and 
after  all  conditions  are  fully  understood  and  considered. 

151.  Impulse  and  Reaction.— A  jet  of  water  spouting  freely  from 
any  orifice  will  acquire  a  velocity  (see  Eq.  9,  Chap.  II). 

(1)  v  =  -/2JpT 

and  will  possess  energy  in  foot  pounds  per  second   (see   Eq.   10, 
Chap.  II)  as  follows: 

Wv8 


3I2 


Hydraulics  of  the  Turbine. 


The  energy  of  the-  jet  leaving  the  orifice  is  the  product  of  a  force, 
F,  which  acting  on  the  weight  of  water,  qw,  for  one  second  gives  it 
the  velocity  v. 

The  space  passed  through  by  the  force  in  one  second,  in  raising 
the  velocity  from  0  to  v  is  (see  Eq.  6,  Chap.  II) 


(3) 


S  =  va  t 


and  the  work  done  in  foot  pounds  is  therefore 
(4)  E  =  FS  =      - 


From  Equations  2  and  4  therefore 

Fv  _  gwv2 
(5)  — -— 9^r- 

(6) 


and  therefore 


F  _  qwv 
g 

The  force,  F,  is  exerted,  by  reaction  on  the  vessel  of  which  the 
orifice  is  a  part  and  may  produce  motion  in  that  vessel  if  it  be  free 
to  move,  or  it  may  produce  motion  in  another  body  by  impulse 
through  the  extinction  of  the  momentum  of  the  jet  in  impinging 
against  it. 

These  equal  and  opposite  forces  are  well  shown: 

ist.  By  the  force  required  to  sustain  a  hose  nozzle  against  the 
reaction  of  a  fire  stream,  and 

2nd.  By  the  force  of  the  jet,  from  the  nozzle  so  sustained  when 
exerted  against  any  object  in  its  course. 

These  conditions  are  illustrated  by  Figs.  198  and  199. 

The  force,  F,  which  may  be  exerted  by  a  jet  impinging  against 
a  surface  depends  on  the  momentum  of  the  moving  stream  of  wa- 
ter and  is  directly  proportional  to  its  velocity.  It  is  also  a  function 


Fig.  198. 


Fig.  199. 


The  Impulse  Wheel. 


3i3 


of  the  angle  through  which  the  jet  is  deflected.  If  friction  be  ig- 
nored, the  stream  will  be  deflected  without  change  in  velocity,  and 
the  force  exerted  against  the  surface  in  the  original  direction  of  the 
jet  will  be  equal  to  the  momentum  of  the  original  stream  less 


Fig.  201. 


Fig.  202. 


Fig.  200. 


the  component,  in  the  original  direction,  of  the  momentum  of  the 
diverted  jet.     (See  Fig.  200). 


(7) 


(1  —  cos  a) 


If  the  jet  impinges  against  a  flat  surface  (see  Fig.  201) 
a  =  90°,  Cos  a  —  0  and 


If  the  jet  is  deflected  180°  by  means  of  a  semi-circular  bucket 
(see  Fig.  202) 

Cos  180°  =  —  1,  and  therefore 

>)  -  *  =  ^ 

152.  The  Impulse  Wheel. — Impulse  water  wheels  utilize  the  im- 
pulsive force  of  a  jet  impinging  against  buckets  attached  to  the 
circumference  of  the  wheel.  The  bucket  must  move  under  the 
impulse  in  order  to  transform  the  energy  of  impact  into  work  and 
the  ratio  of  v',  the  velocity  of  the  periphery  of  wheel,  to  the  velocity 
v  of  the  jet  is  indicated  by  #  4f 


(10) 


tp  =  —  and  v '  =  q>  v 


19 


314 


Hydraulics  of  the  Turbine. 


In  determining  the  force,  F,  exerted  upon  the  moving  bucket,  the 
relative  instead  of  the  actual  velocity  of  the  jet  must  be  considered 

and  it  is  readily  seen  that  the 
value  of  the  relative  velocity  vr 
will  be  as  follows: 


(11) 


vr  =  v  —  <?  v  =  (1  — 


The  relative  weight  of  water 
that  strikes  a  single  bucket  per 
second  will  also  be  less  on  ac- 
count of  the  movement  of  the 
buckets,  but  as.  new  buckets  con- 
stantly intercept  the  path  of  the 
jet  the  total  amount  of  water 

effective  is  equal  to  the  total  discharge  of  the  jet.      Hence  from 

equations  (7  and  11) 


Fi 


(12) 


F  =  (1  —  cos  a) 


(1  —  <p) 


The  work  done  upon  the  buckets  per  second  is  equal  to  the  force, 
F,  times  the  distance  <£  v  through  which  it  acts,  i.  e. 


(13) 


E  = 


=  (1  —  cos  a)  (1 


is  a  maximum  the  solution 


This  is  a  maximum  when  (1  —  < 
of  which  gives  #  =  .5 

Substituting  4>  =  .$  and    a  =180°,   in  equation    (13),  there   is  ob- 
tained 


(14) 


E  = 


q  wv- 


That  is,  E  equals  the  entire  energy  of  the  jet  (see  equation  2),  and 
hence  the  theoretical  efficiency  when  (£=0.5  is  100  per  cent. 

Another  criterion  for  maximum  efficiency  is  that  the  absolute 
velocity  of  the  water  in  leaving  the  bucket  must  be  zero. 

When  a  =180°,  the  absolute  velocity  with  which  the  water 
leaves  the  bucket  is  evidently  the  velocity  relative  to  the  bucket 
minus  the  velocity  of  the  bucket  or 


(15)  v 

This  gives 


=  (1  —  <p)  v  —  (pv  =  v  —  2<p  v  =  0 


Effect  of  Angle  of  Discharge  on  Efficiency.  315 

153.  Effect  of  Angle  of  Discharge  on  Efficiency.  —  In  an  impulse 
wheel  it  is  not  practicable  to  change  the  direction  of  the  water 
through  180°  as  it  would  then  interfere  with  the  succeeding  bucket. 
a  must  hence  be  less  than  180°  and  the  absolute  velocity  of  the 
water  in  leaving  the  buckets  cannot  be  zero.  The  loss  from  this 
source  is  small  as  a  may  differ  considerably  from  180°  without 
much  effect  on  the  bucket  pressure  and  hence  on  the  efficiency. 
For  example,  —  the  ratio  of  actual  pressure  when  a  is  less  than 
1  80°  to  maximum  possible  pressure  with  a  =180°  is  (see  Fig.  203). 

(1  —  cos  a)  qw  (I  —  <p]  (1  ~  *)  V 
,  A      '  '          g  1  —  cos  a  _  1  +  cos  ft 


If  ft  =  8°,     a  =  172°,  and  1  ~  f,°S  a   =  .995 

6 

showing  only  0.5  per  cent,  reduction.     The  effect  on  the  efficiency 
is  in  the  same  ratio. 

Fig.  204  illustrates  the  flow  o'f  the  water  in  entering  and  leaving 
the  bucket  with  all  velocities  given  relative  to  that  of  the  bucket. 
The  jet  leaves  the  bucket  as  shown  with  a  relative  velocity  of  (i  —  <£) 
v.  If  this  velocity  is  combined  graphically  with  the  velocity  of 
the  bucket,  <£v,  the  true  absolute  residual  velocity  VR  of  the  water 
will  be  obtained.  The  efficiency  is  evidently  maximum  when  <£  has 
a  value  which  makes  VR  a  minimum.  This  condition  can  readily 
be  shown  to  maintain  when  the  triangle  is  isoceles  or  when 

(17)  <pv  =  (i-<f>)v 

which  gives 

(p  =  0.5 

as  obtained  by  two  other  methods  and  here  shown  to  be  indepen- 
dent of  the  angle  ft. 

The  absolute  path  of  the  water  in  space  is  shown  by  ABCD  Fig. 
204,  and  the  magnitude  of  this  velocity  is  shown  below  in  curve  EF 
where  ordinates  are  absolute  velocities  along  the  tangent  lines  to 
curve  ABCD  at  the  point  directly  above.  These  curves  are  based 
on  the  assumption  that  <£—  0.5  and  the  bucket  is  semi-circular  in 
cross  s'ection  as  shown. 

The  theoretical  considerations  thus  far  discussed  are  modified  by 
the  frictional  resistance  which  the  bucket  offers  to  the  flow  of  wa- 
ter over  its  surface  and  by  the  spreading  of  the  original  jet  from 
its  semi-circular  section  to  a  wide  thin  layer  in  leaving  the  bucket. 


Hydraulics  of  the  Turbine. 


Further  loss  no  doubt  takes  place  as  a  result  of  the  fact  that  the 
bucket  is  in  its  assumed  position  at  right  angles  to  the  direction 
of  the  jet  only  at  one  instant  during  its  rotation.  Upon  entering 


D 


Fig.  204. 

and  leaving  the  jet  it  is  inclined  considerably  to  this  direction  and 
doubtless  operates  less  efficiently.  These  conditions  result  in  a 
much  greater  drop  in  efficiency  than  the  above  analysis  would 
seem  to  indicate. 

154.  Reaction  Wheel — The  flow  of  water  through  the  buckets  of 
a  reaction  wheel  is  less  easily  analyzed  than  in  the  case  of  the  im- 
pulse wheel.  The  chief  difference  in  the  two  types  of  wheels  arises 


Reaction  Wheel. 


from  the  fact  that  the  reaction  wheel  is  "filled"  and  hence  the  ve- 
locity of  the  water  relative  to  the  buckets  at  any  point  does  not 
remain  constant  but  varies  inversely  as  the  cross  sectional  area  of 
the  passageway. 

The  path  described  by  a  particle  of  water  in  passing  through  the 


Fig.  205. 

wheel  has  been  investigated  by  Francis,*  by  a  method  based  upon 
the  assumption  that  "every  particle  of  water  contained  in  the 
wheel,  situated  at  the  same  distance  from  the  axis,  moves  in  the 
same  direction  relative  to  the  radius  and  with  the  same  velocity." 
This  assumption  becomes  more  accurate  as  the  number  of  buckets 
increases. 

Fig.  205  shows  the  path,  resulting  from  the  application  of  this 
assumption,  of  the  water  through  the  "Tremont"  Fourneyron  wheel 
and  Fig.  206,  through  the  center  vent  wheel  a.t  the  Boott  Cotton 
Mills.  The  former  indicates,  since  the  jet  of  water  is  carried  for- 
ward in  the  direction  of  rotation,  that  the  water  resists  the  rota- 


Fig.  206. 


*  See  "Lowell  Hydraulic  Experiments,"  p.  39. 


Hydraulics  of  the  Turbine. 


Fig.  207. 


tion  of  the  wheel  until  nearly  to  the  circumference  when  it  is  sud- 
denly deflected  and  leaves  the  wheel,  as  it  should,  in  a  direction 
nearly  normal  to  the  wheel. 

The  jet  of  water  in  the  Boott  wheel  (Fig.  206),  on  the  other 
hand,  shows  a  continual  backward  deflection  of  its  path  from  the 

point  where  it  leaves  the  guides,  and 
hence  a  continual  delivery  of  its 
energy  to  the  wheel.  This  seems  to 
indicate  a  more  logical  condition  and 
.  a  better  shaped  bucket  than  that  of 
the  Fourneyron.  It  will  be  noted 
that  the  actual  path  of  the  water  in 
this  case  is  very  similar  to  that  in  the 
impulse  wheel  shown  in  Fig.  204. 

For  the  economical  operation  of 
the  reaction  wheel  the  following 
principles  must  be  observed: 

I  St.  In  order  that  the  jet  of  water  may  enter  the  wheel  without 
shock  the  resultant  of  the  velocity  of  the  water  as  it  leaves  the 
guides  and  the  velocity  of  the  periphery  of  the  runner  must  have 
a  direction  parallel  to  the  bucket  blades  at  this  point,  and  a  mag» 
nitude  equal  to  that  which  will  produce  the  required  discharge 
through  the  cross  sectional  area  of  the  passageway. 

2nd.  The  relative  velocity  of  the  bucket  and  of  the  water  relative 
to  the  bucket  at  the  point  of  discharge  must  be  such  that  the  water 
leaves  the  buckets  with  the  minimum  practicable  absolute  velocity. 
3rd.  Such  residual  velocity  as  may  remain  in  the  discharging  wa- 
ter must  be  conserved  and  utilized  as  far  as  practicable  by  the 
proper  arrangement  of  the  draft  tube. 

4th.  In  all  wheels  it  is  also  essential  by  proper  design  to  reduce 
losses  from  friction,  eddying,  etc.,  as  greatly  as  possible. 

The  first  requirement  is  illustrated  in  Fig.  207  where  AB  is  one 
of  the  runner  buckets  of  an  outward  flow  wheel.  The  guides,  AC, 
direct  the  water  into  the  buckets  with  an  absolute  velocity,  v2.  The 
velocity  of  the  runner  at  point  A,  where  the  water  enters,  is  u2. 
The  two  velocities  combined  graphically  give  a  resultant,  vr,  which 
must  be  tangent  to  the  curve  of  the  bucket  and  equal  to 

(18)  v  —  9.2    where 

*  Q 


q3  =  required  discharge  through  the  passageway,  and 

a2  =  area  of  cross  section  of  the  passageway  at  point  of  entrance,  A. 


Reaction  Wheel.  319 

This  requirement  does  not  enter  into  the  design  of  an  impulse 
wheel  since  the  jet  impinges  against  the  edge  of  the  wedge-shaped 
partition  in  the  bucket  always  in  a  direction  tangent  to  the  bucket 
curve  at  that  point  regardless  of  the  relative  speeds  of  runner  and 
jet.  Further,  since  the  discharge  is  "free"  and  the  buckets  not 
"rilled,"  no  sudden  change  of  velocity  occurs. 

The  effect  of  part  gate  conditions  upon  the  first  requirement  de- 
pends upon  the  type  of  speed  gate  and  may  best  be  studied  from 
Figs.  188,  191,  193  and  207.  A  change  in  either  direction  or  mag- 
nitude of  vl  will  change  vr  unless  the  two  effects  tend  to  neutralize 
which  may  happen  in  some  instances.  In  all  reaction  wheels  the 
velocity  of  inflow,  v15  through  the  guides  is  increased  by  partly 
closing  the  gate,  while  the  velocity,  Ui,  of  the  wheel  remain  un- 
changed. vr  will  therefore  change,  and  a  change  in  either  its  direc- 
tion or  magnitude  will  produce  an  impact  or  sudden  enlargement 
respectively-  as  the  water  enters  the  runner,  and  therefore  a  loss, 
unless  the  direction  of  the  guides  is  changed  to  correspond. 

The  wicket  gate,  when  carefully  designed,  has  given  rise  to  part 
gate  efficiencies  more  nearly  approaching  those  of  impulse  wheels 
than  with  gates  of  any  other  type  (see  Figs.  131  and  236). 

The  second  requirement,  that  of  minimum  residual  velocity  of 
the  water  in  leaving  the  buckets,  is  shown  graphically  in  Fig.  207. 
VR  is  the  velocity  of  discharge  of  the  water  relative  to  the  bucket 
and  is,  of  course,  tangent  to  the  curve  of  the  bucket.  u2  is  the 
peripheral  velocity  of  the  runner.  The  resultant  of  two  velocities 
is  the  absolute  velocity  with  which  the  water  is  discharged  from  the 
wheel,  and  is  shown  in  magnitude  and  direction  by  line  v2.  Now,  at 
part  gate  the  quantity  of  water  discharged  is  less  than  that  at  full 
gate  and  hence  VR  must  also  be  less  since  the  cross  section  of  the 
passage  must  be  filled.  u2  remains  unchanged  and  hence  the  resul- 
tant v2  will  be  increased  with  a  corresponding  waste  of  energy  and 
loss  in  efficiency.  This  is  an  unavoidable  loss  in  a  wheel  operating 
under  part  load  and  makes  it  impossible  to  maintain  full  efficiency  of 
operation  by  any  design  whatever  of  the  regulating  gates.  This 
loss  does  not  appear  in  the  impulse  wheel  since  the  velocity  with 
which  the  water  leaves  the  bucket  is  theoretically  at  least  not  in- 
fluenced by  the  quantity. 

The  third  requirement  is  partially  satisfied  by  gradually  expand- 
ing the  draft  tube  from  the  wheel  to  the  point  of  discharge.  This 
will  recover  only  the  component  of  the  residual  velocity  in  the  axial 


320 


Hydraulics  of  the  Turbine. 


direction.     The  larger  component  of  the  residual  velocity  however 
tends  to  produce  a  rotation  of  the  water  column  in. the  draft  tube, 
and  is  not  recovered  by  any  present  design. 
The  fourth  requirement  is  evident. 


L.3 


Figs.  208-209. — Reaction  Wheel  with  Concrete  Draft  Tube.* 


100 


TOTAL     AVAILABLE     ENERGY 


ENTRANCE      .GATES 


Fig.  210.— Graphical  Relation  of  Velocity  and  Energy  in  the  Flow  Through 

a  Reaction  Turbine  with  Draft  Tube. 
*  Turbinen  and  Turbinenanlagen,  Viktor  Gelpke-,  page  61. 


Energy  Transformation,  Reaction  Turbine.  321 

155.  Graphical  Relation  of  Energy  and  Velocity  in  Reaction  Tur- 
bine.— The  relations  of  the  changes  in  velocity  and  in  energy  in  the 
passage  of  water  through  a  reaction  turbine  and  its  draft  tube  are 
graphically  shown  in  Fig.  210.. 

Fig.  208  shows  the  cross  section  of  a  radial  inward  flow  reaction 
turbine  with  a  concrete  draft  tube.  The  cross  sections  of  the  draft 
tubes  at  various  points  are  shown  in  Fig.  209  from  which  it  will 
be  seen  that  the  draft  tube  of  this  turbine  gradually  changes  form 
and  increases  in  cross  section  in  order  that  the  velocity  of  flow  may 
be  gradually  decreased  from  the  point  of  discharge  of  the  turbine 
to  the  end  of  the  draft  tube. 

The  changes  in  absolute  velocity  in  the  passage  of  water  into  and 
through  the  turbine  and  draft  tube  are  shown  by  line  V,  Vx,  V2,  V4, 
V5 ;  the  height  of  the  ordinates  at  these  points  shows  the  approxi- 
mate absolute  velocities  at  such  points  in  the  flow.  The  absolute 
velocity  is  a  maximum  at  or  near  the  point  where  the  water  enters 
the  runner  and  is  decreased  as  greatly  as  possible  at  the  point  of 
its  discharge  into  the  draft  tube.  By  gradually  increasing  the  area 
of  the  draft  tube,  an  additional  reduction  in  velocity  is  obtained, 
the  water  finally  issuing  with  a  velocity  V5.  The  maximum  veloc- 
ity, measured  by  the  ordinate  V2,  is,  in  reaction  wheels,  consider- 
ably below  the  spouting  velocity  (i/2gh) 

In  its  flow  through  the  wheel,  the  velocity  of  the  water  relative 
to  the  bucket  increases  and  becomes  a  maximum  at  the  outlet  of 
the  wheel.  This  increase  in  relative  velocity  is  shown  by  the  line 
V,,  V.. 

The  energy  transformation  which  takes  place  during  the  change 
in  velocity  is  illustrated  by  the  dotted  line  marked  "Energy  trans- 
formation" which  begins  at  a  maximum  of  100  per  cent,  at  the  en- 
trance of  the  wheel ;  is  decreased  by  friction,  leakage,  shocks,  etc., 
by  about  16  per  cent,  under  full  gate  conditions.  The  energy  is 
transformed  into  useful  work  in  the  wheel  by  the  reaction  at  the 
point  of  discharge  and  utilizes  about  80  per  cent,  of  such  energy, 
the  remaining  4  per  cent,  being  rejected  in  the  discharge  from  the 
draft  tube  with  a  slight  recovery  of  velocity  energy  as  before  de- 
scribed. 

156.  Turbine  Relations. — In  all  water  wheels  the  quantity  of  dis- 
charge, the  power,  speed,  efficiency  and  effective  head  on  the  wheel 
are  closely  related  and  vary  in  accordance  with  certain  definite  laws 
modified  by  the  design  of  the  turbine  and  the   conditions  under 


322 


Hydraulics  of  the  Turbine. 


which  it  is  operated.  The  conditions  of  operation  must  be  adapted 
to  the  type  of  machinery  used,  or  the  machinery  must  be  selected  in 
accordance  with  the  conditions  under  which  it  must  operate,  in  or- 
der that  the  best  results  may  be  attained. 

If  a  jet  or  stream  of  water,  with  a  velocity,  v,  acts  on  the  moving 
surface  of  a  motor  bucket,  this  bucket,  if  the  friction  of  the  wheel  is 
negligible,  may  acquire  a  velocity  essentially  equal  to  that  of  the 
jet,  i.  e.,  to  the  theoretical  velocity  due  to  the  head.  In  actual  prac- 
tice the  velocity  of  the  bucket  will  always  be  less  by  the  amount  of 
velocity  lost  in  overcoming  the  friction  of  the  wheel.  The  velocity 
of  the  wheel  here  considered  must  be  measured  at  the  center  of  ap- 
plication of  the  forces,  i.  e.,  at  the  point  of  application  of  the  result- 
ant of  all  the  forces  of  all  the  filaments  of  water  that  act  on  the 
wheel.  Under  conditions  where  the  resultant  velocity  of  water  and 
bucket  are  the  same,  it  is  evident  that  the  water  will  produce  no 
pressure  o-n  the  bucket  and  the  motor  can  deliver  no  power.  As 
soon  as  resistance  occurs,  the  speed  of  the  wheel  is  reduced.  Under 
reduced  speed  the  momentum  of  the  jet,  or  the  reactive  pressure  of 
the  water,  according  to  the  circumstances  of  design,  is  converted 
into  power.  This  impact  or  pressure  increases  as  the  speed  or  ve- 
locity of  the  bucket  decreases  until  the  maximum  impact  or  pres- 
sure results  with  the  bucket  at  rest,  in  which  case  also  no  work  is 
done.  At  some  speed,  therefore,  between  these  extremes  the  maxi- 


90 


BP 


§30 


80  80  100 

REVOLUTIONS        PER        MINUTE 


140 


Fig.  211. — Efficiency  Speed  Curves  of  a  48"  "Victor  Turbine." 


Turbine  Relations. 


323 


•& 

II 


IS  , 
Ip  2 


<  », 


\ 


*-* 


\\ 


o     or 


hU 


o  $ 

>  ft 

a:  ^ 
P 

o 


000000 
^  C4  O  CD  (O  * 

QV2H    100J   fJ331ti!HJ.  d3QNR   b3A\Od    3SUOH 


324  Hydraulics  of  the  Turbine. 

mum  amount  of  work,  from  a  given  motor,  will  be  obtained.  That 
is  to  say, — at  a  certain  fixed  speed  the  maximum  work  and  the  maxi- 
mum efficiency  of  a  given  wheel  will  be  obtained,  and  at  any  speed 
below  or  above  this  speed,  the  power  and  efficiency  of  the  wheel 
will  be  reduced.  These  conditions  vary  considerably  according  to 
the  type  and  design  of  the  wheel  considered  and  also  according  to 
the  gate  opening  at  which  the  wheel  may  be  operated. 

The  efficiency  curves  of  a  48"  Victor  turbine,  under  a  thirteen 
foot  head  and  under  various  conditions  of  gate,  are  shown  in  Fig. 
211.  Fig.  212  shows  the  <£-power  cttrve  of  the  same  wheel  under 
the  same  conditions  of  head  and  gates. 

157.  Relation  of  Turbine  Speed  to  Diameter  and  Head. — The 
velocity  of  the  periphery  of  the  impeller  or  buckets  of  a  wheel  is 
not  necessarily  and  in  fact  is  not  usually  the  same  as  the  velocity  of 
the  point  of  application  of  the  resultant  of  the  forces  applied  to  the 
wheel.  This  point  may  be  at  some  considerable  distance  within  the 
wheel  and  at  a  point  not  easily  determined.  This  point  of  applica- 
tion of  the  resultant  forces  may  vary  in  position  with  the  gate  open- 
ing. The  peripheral  diameter  is  fixed  and  is  therefore  more  conve- 
nient for  consideration  than  the  point  of  application  of  the  forces. 
The  peripheral  diameter,  or  the  catalogued  diameter,  is  therefore 
used  in  the  discussion  of  the  general  subject.  Many  wheels  vary  in 
diameter  at  various  points  on  the  periphery  (see  Fig.  174),  and  there 
is  no  uniform  practice  among  manufacturers  in  designating  such  di- 
ameters so  that  the  diameters  used  in  the  following  discussion  and 
the  functions  based  thereon  are  in  accordance  with  the  practice  of 
each  maker  and  are  therefore  not  strictly  comparative.  In  this  dis- 
cussion the  laws  discussed  are  equally  true  if  based  on  any  actual 
diameter  or  any  simple  function  of  the  same.  The  diameter  chosen 
simply  influences  the  magnitude  of  the  derived  function  and  not  the 
character.  The  discussion  holds  therefore  in  each  case  regardless  of 
the  method  of  measurement  except  for  the  purpose  of  comparison 
between  wheels  of  various  makers  in  which  case  similar  diameters 
must  be  used. 

In  reaction  wheels,  the  buckets  extend  from  the  periphery  of  the 
wheel  to  a  point  quite  near  the  axis  of  revolution  (see  Fig.  128, 
Diagram  I).  In  such  wheels  the  resultant  of  the  forces  applied  falls 
a  considerable  distance  within  the  circumference  of  the  wheel.  In 
such  wheels  the  peripheral  velocity  may  exceed  the  velocity  of  the 
jet  acting  on  the  wheel.  In  impulse  wheels  (see  Fig.  129,  Diagram 
E)  the  buckets  are  small  in  comparison  to  the  wheel  diameter  and 


Relation  of  Speed  to  Diameter  and  Head.  325 

are  located  at  the  periphery;  hence,  in  this  class  of  wheels,  the  re- 
sultant of  the  forces  applied  lies  at  or  near  the  periphery,  and  the 
peripheral  velocity  will  be  less  than  that  of  the  jet  acting  on  the 
wheel. 

Taking  the  velocity  of  the  periphery  of  the  wheel  as  a  function 
of  the  velocity  due  to  head,  the  relations  may  be  expressed  by  the 
formula : 

(19)  v'  =  <Pi/2gh~        from  which 

v'          v' 


(20)  <p  = 


l/2gh 


The  velocity  of  the  periphery  of  the  impeller  may  be  expressed 
by  the  following  formula  : 

_    D*n    ._  3.1416  D  n 
'   12  x  60  ~          720 

Combining  equations  (20)  and  (21)  it  follows  that: 

3.1416  D  n  D  n 

(22)  *  =  720xb.025v/F  =  -000543  7^ 

From  this  may  also  be  written: 

—     <P  ^h"     —     1841.  6  <?•/£" 


(23) 


.000543  D  D 

As  equation  (22)  is  general,  it  follows  that  when  V~q>  is  constant: 

D  n 

(24)  —r=*  —  1841.6  cp  =  A  is  constant. 

v  n 

If  h  — I,  this  will  reduce  to: 

(25)  D  nj  =  1841.6  <p  =  A 

The  catalogue  speed,  power  and  discharge  of  each  series  of 
wheels,  as  given  in  the  catalogues  of  manufacturers,  are  usually 
based  on  the  conditions  of  maximum  efficiency  and  constant  <£. 

From  the  above  considerations  it  follows  that  in  any  homogen- 
eous series  of  wheels,  that  is  in  any  series  of  wheels  constructed  on 
uniform  lines  and  with  dimensions  proportional,  the  wheels  of  the 
series  are  designed  to  run  at  the  same  relative  velocity,  and  there- 
fore 

D  n        D!  nt 

(26)  Vb~  ~      I/IT 


326 


Hydraulics  of  the  Turbine. 


That  is  to  say :  In  any  homogeneous  series  of  turbines  the  pro- 
duct of  the  diameter  of  any  wheel  D,  and  the  number  of  revolutions 
n}  divided  by  VW  will  be  a  constant  A  provided  <£  remains  constant. 

In  investigating  the  values  of  A  and  <j>  for  various  makes  of 
wheels,  as  expressed  by  the  data  in  the  manufacturers'  catalogues, 
it  is  found  that  these  values  vary  somewhat  for  different  wheels  of 
a  series  but  are  usually  practically  constant.  It  will  be  noted, 
however,  from  the  efficiency  speed  curve,  shown  in  Fig.  211,  and 
the  <j>  power  curve,  shown  in  Fig.  212,  that  the  speed,  and  conse- 
quently the  values  of  <f>  and  A,  may  vary  somewhat  without  materi- 
ally affecting  the  efficiency  or  power  of  the  wheel. 

It  should  also  be  noted  from  Figs.  211  and  212  that  if  it  is  de- 
sired to  secure  the  greatest  efficiency  and  power  at  part  gate,  the 
values  of  <f>  and  A  for  a  given  wheel  must  be  reduced.  Table 
XXVI  gives  the  values  of  A  and  <f>  for  various  American  wheels, 
calculated  from  the  catalogues  of  the  manufacturers. 

TABLE  XXVI. 

Showing  Relation  of  Diameter  and  Speed  of  Various  American  Turbines  working 
under  Catalogue  Conditions. 

_  D  n  _  v^=     D  n 

Vh  v 


"Worno  r»f  Whool 

L 

^ 

c/ 

3 

Min. 

Max. 

Min. 

Max. 

Reaction  Wheels. 
T.  C.  Alcott  &  Son... 

Alcott's    Standard 
High  Duty  

1210 

1254 

.658 

.682 

Alcott's  Special  High 
Duty 

1211 

1253 

.658 

.682 

Alexander,  Bradley  & 
Dunning  

Syracuse  Turbine 

1203 

1226 

.654 

666 

American  Steel  Dredge 
Works  

Little  Giant 

1235 

1462 

671 

794 

Camden  Water  Wheel 
Works. 

United  States  Turbine 

1372 

1588 

745 

864 

Chase  Turbine  Mfg.  Co. 

Christiana    Machine 
Co  

*Chase-Jonval      Tur- 
bine (regular)  
*Chase-Jonval      Tur- 
bine (special)  

Balanced    Gate    Tur- 

1612 
1840 

1997 
2237 

.876 
.999 

1.084 
1.2H 

bine  

1220 

1298 

.663 

.706 

*NOTE.— Wide  variation  in  constants  due  to  the  design  being  special  for  various  sized  wheels 
(series  not  exactly  homogeneous). 


Relation  of  Speed  to  Diameter  and  Head. 


327 


TABLE  XXVI— Continued 

Showing  Relation  of  Diameter  and  Speed  of  Various  American  Turbines  working 
under  Catalogue  Conditions. 

D  n  v'  D  n 

A  =  -/==  q>=—  =  .000543  —7= 

V\\  v  Vh 


t 

S 

<7 

3 

Manufacturer. 

Min. 

Max. 

Min. 

Max. 

Reaction  Wheel—  Con. 

Craig  Ridgway  &  Son 
Co  

Double  Perfection  

1186 

1250 

.614 

.679 

Craig  Ridgway  &  Son 
Co 

Standard  

1200 

1275 

652 

693 

Dayton  Globe  Iron 
Works  Co  

American  Turbine... 

1218 

1295 

.662 

.704 

fNew  American  Tur- 
bine    (high      head 
type)  

1064 

1077 

.578 

.585 

Improved  New  Amer- 
ican          

1632 

1738 

.886 

.944 

J.  L.  &S.  B.  Dix  

Special  New  American 
Improved  Jonval  Tur- 
bine 

1284 
1474 

1340 
1617 

.697 
800 

.727 
880 

Dubuque    Turbine    & 
Roller  Mill  Co  
Dubuque  Turbine  & 
Roller  Mill  Co 

Flenniken  Turbine... 
McCormick'sHolyoke 

1511 

1533 

.821 

.833 

Turbine 

1196 

1296 

650 

704 

Humphrey  Machine 
Co  

Hercules  Turbine.  .  .  . 
JIXL  Turbine  

1160 
1198 

1170 
1209 

.630 
.652 

.636 
.657 

JXLCR  Turbine  

1196 

1206 

.652 

.656 

Rodney  Hunt  Ma- 
chine Co 

McCormick    Holyoke 

Turbine           

1159 

1278 

.630 

.694 

Hunt  McCormick  Tur- 
bine   

1158 

1272 

.629 

.691 

New  Pattern  Hunt 
Turbine 

1163 

1415 

.632 

.768 

Standard  Wheel,  1887 
Pattern            

1200 

1291 

.651 

.701 

E.  D.  Jones  &  Sons  Co. 
James  Leffel  &  Co  .  .    . 

Crocker  Wheel  
Samson  Wrater  Wheel 
Improved  Samson  
Standard             

1208 
1543 
1578 
1330 

1292 
1554 
1H32 
1339 

.657 

.  838 
.  856 
.  7'2>2 

.702 
.84* 
.886 
.727 

Special             

1380 

1434 

.750 

.  779 

Munson  Bros.  Co  

Phoenix  "Little 
Giant".. 

1001 

1020 

.544 

.554 

tCatalogue  recommends  a  maximum  and  minimum 
age  speed. 

^Tables  based  on  full  theoretical  power  of  the  water, 
to  90  per  cent  efficiency,  depending  on  location. 


speed.    Constants  given  are  for  the  aver- 
Wheels  are  said  to  give  from  75  per  cent 


328 


Hydraulics  of  the  Turbine. 


TABLE  XXVI.— Continued. 

Showing  Relation  of  Diameter  and  Speed  of  Various  American  Turbines 
working  under  Catalogue  Conditions. 


A  = 


Dn 
Vh 


=   .000543      JL 

i/h 


'I 

i. 

< 

p 

Manufacturer. 

^•ame  01  wneei. 

Min. 

Max. 

Min. 

Max. 

Reaction  Wheel—  Con. 

Norrish,    Burnham  & 
Co 

1213 

1233 

659 

670 

Platt  Iron  Works  Co.  . 

Victor  Register  Gate. 
Victor  Standard  Cyl- 

1181 
1380 

1221 
1410 

.641 
.749 

.663 

.765 

Poole  Engineering  & 
Machine  Co 

Poole-Leffel  

1341 

1380  " 

728 

749 

T.  H.  Risdon  &  Co.  ... 

Risdon  Standard  
Risdon  Turbine  Type 
T  C 

1213 
1213 

1420 
1420 

.659 
659 

.772 
772 

Ris.don  Turbine  Type 
D.  C  

1213 

1420 

.659 

.772 

S.  Morgan  Smith  Co  .  . 

Smith-McCormick  .  .  . 
Smith 

1180 
1655 

1344 
1679 

.641 

898 

.730 
911 

Trump  Mfg.  Co  

Standard  Trump 

1320 

1380 

.716 

749 

Wellman,  Seaver, 
IMorgan  Co 

McCormick 

1212 

1260 

658 

684 

Impulse  Wheels. 

DeRemer  Water 
Wheel  Co  

DeRemer  Water 

Wheel  

962 

1001 

.522 

.545 

Abner  Doble  Co  

Tangential  \Vheel 

841 

848 

456 

460 

Pelton  Water  Wheel 
Co 

Tangential  Wheel 

912 

92] 

495 

500 

Platt  Iron  Works  Co.. 
The  Risdon  Iron  Wks. 

Victor  High  Pressure 
Tangential  Wheel  

915 

917 

919 
920 

.497 
.498 

.499 
.499 

From  equation  (26)  may  be  derived 
(27)  „  =  ^ff- 

From  this  equation  the  economical  speed  or  correct  number  of 
revolutions  n  for  any  wheel  of  diameter  D,  at  any  head,  i/F,  can 
be  obtained  if  the  revolutions  n±  of  any  other  wheel  of  the  series 
at  head  h,  and  of  diameter  D,  is  known. 


Relations  of  0  and  Efficiency.  329 

If  in  equation  (27),  D  =  Da,  the  equation  reduces  to 

(28)  n-    ^Eor^  =  -^ 

T/hi  Vh  T/hi 

That  is  to  say :  The  economical  speed  of  any  wheel  will  be  in  direct 
proportion  to  the  square  root  of  the  head  under  which  it  acts. 
If  in  the  equation  (28),  n  —  1,  the  equation  reduces  to 
(39)  n       nlV/K 

From  which  it  follows  that  tLe  revolutions  of  a  wheel  (n)  for  any 
head,  h,  is  equal  to  the  evolutions  nx  for  one  foot  head  multiplied 
by  Vh. 

158.  Graphical  Expression  of   Speed   Relations. — The   relation 
expressed  by  equations  18  to  27,  inclusive,  between  the  values  of  v, 
<£,  D,  n,  and  h,  are  graphically  shown  by  Fig.  213.     The  theoretical 
relations  between  v'  and  h,  and  <j>  as  expressed  by  equation   (19) 
when  4>-—i,  are  represented  by  the  upper  curved  line  in  the  diagram 
referred  to  ordinates  and  abcissas.    The  relation  between  </>,  v  and  h, 
where  <f>  has  a  fractional  value  or  is  less  than  100  per  cent.,  as  is  the 
case  for  all  wheels  working  under  practical  conditions,  is  shown  by 
reference  to  the  curved  lines  below ;  the  fractional  value  of  <f>  as  rep- 
resented by  each  line  is  given  thereon.    The  relations  between  v,  D 
and  n  are  shown  by  the  relations  of  the  straight  lines  originating 
near  the  lower  right-hand  corner  of  the  diagram  referred  ta  ordi- 
nates and  abcissas,  and  the  mutual  relations  of  all  lines  on  the  dia- 
grams show  the  mutual  relations  between  the  various  factors  that 
are  here  considered. 

159.  Relations   of  <£   and   Efficiency.— In   any  turbine   running 
under  different  heads  but  otherwise  under  the  same  physical  condi- 
tions as  to  gate  opening,  setting,  draft  tubes,  etc.,  the  efficiency  will 
remain  constant  provided  the  ratio  of  the  velocity  of  rotation  to  the 
theoretical  spouting  velocity  of  the  water  under  the  given  head 
remains  the  same.     This  is  to  say, — the  efficiency  of  a  wheel  will 
remain  constant  under  various  conditions  of  head  as  long  as  the 
value  of  <£  remains  constant.    This  law  is  well  demonstrated  by  ex- 
periments made  on  a  12"  Morgan-Smith  wheel  at  the  Hydraulic 
Laboratory  of  the  University  of  Wisconsin.*    These  experiments 
were  made  under  seven  different  heads  varying  from  about  7.10  feet 
to  about  4.25  feet.     The  results  of  all  these  experiments  have  been 


*  "Test  of  a  Twelve-Inch  McCormick  Turbine,"  an  unpublished  thesis  by 
O.  W.  Middleton  and  J.  C.  Whelan. 
20 


330 


Hydraulics  of  the  Turbine. 


REVOLUTIONS     PER     MINUTE 

Fig    213.— Speed  Relations  of  the  Turbines. 


Relations  of  0  and  Efficiency. 


0.0      O.I       0.2     0.3     0.4      0.5     0.6     0.7     0.8     0.9       1.0       1. 1 
VALUES     OF     $ 

Fig.  214. — Efficiency—^  Curve  of  a  12  "Smith-McCormick  Turbine. 


332  Hydraulics  of  the  Turbine. 

platted  in  a  single  diagram  (see  Fig.  214)  from  which  it  will  be 
noted  that  all  experiments  are  fairly  close  to  the  mean  curve ;  that 
the  variation  therefrom  is  probably  due  to  experimental  errors 
(principally,  it  is  believed,  in  the  determination  of  the  relative 
velocities)  and  that  reduction  in  head  shows  no  uniform  decrease 
in  efficiency.  The  experiments  referred  to,  which  are  soon  to  be 
published  in  a  University  bulletin,  show  that  this  law  is  true  under 
all  conditions  of  gate  as  well  as  for  the  full  gate  conditions,  illus- 
trated in  Fig.  214.  Hence  the  conclusion  may  be  drawn  that  the 
efficiency  of  a  wheel  will  remain  essentially  constant  if  <£  remains 
constant  at  least  under  moderate  changes  in  head. 

160.  Discharge  of  a  Turbine  at  Fixed  Gate  Opening. — The  dis- 
charge of  a  turbine  with  fixed  gate  opening,  but  at  various  speeds, 
is  not  always  the  same  but  varies  within  certain  limits  and  as  the 
speed  varies.  In  some  cases  the  discharge  of  a  wheel  increases  as 
the  speed  increases.  (See  discharge  of  Tremont  turbine,  Fig.  215.) 
Sometimes  the  discharge  decreases  as  the  speed  increases  (see  dis- 
charge of  Victor  and  McCormick  turbines,  Fig.  215),  and  some- 
times the  discharge  increases  with  the  speed  to  a  certain  point  and 
then  decreases  with  a  further  increase  in  the  speed  (see  discharge  of 
Samson;  and  New  American  wheels,  Fig.  215.) 

In  reaction  turbines  the  discharge  takes  place  first  through  the 
guide  from  which  it  passes  into  and  through  the  buckets  of  the 
wheel.  The  relations  of  these  two  sets  of  orifices  change  as  the 
speed  of  the  wheel  changes  and  affects  the  total  discharge.  If  dur- 
ing such  changes  of  speed,  the  ratio,  $-  — ,  remains  constant,  it 
is  found  by  experiment  that  the  conditions  remain  similar  to  thost; 
of  any  short  tube  or  orifice.  The  discharge  of  a  turbine  may  there- 
fore be  determined  by  the  formula  : 
(30)  q  =  Cat/2jh 

And  it  may  be  stated :  In  a  given  turbine  with  fixed  gate  opening, 
the  discharge  will  be  proportional  to  the  square  root  of  the  head, 
i.  e.,  the  discharge  divided  by  Vh    is  constant. 

The  values  of  C  and  a  vary  with  the  opening  of  the  gate  or  gates, 
but  for  any  one  position  are  essentially  constant. 

Let  the  discharge  of  a  wheel  under  fixed  gate  conditions  and  with 
a  given  head,  ha,  be  given  by  the  formula: 

C3i;  q,  = 


Discharge  of  a  Turbine  at  Fixed  Gate  Opening.  333 

The  discharge  of  any  other  head  will  be  proportional  to  i/h"  and 
therefore 


—  — T=  hence 


(32) 
(33) 


(34)  q  = 

Therefore,  it  may  be  stated :  In  a  given  turbine  with  fixed  gate 
opening  the  discharge  at  any  head  h  will  be  equal  to  the  discharge  at 
one  foot  head  multiplied  by  -\/h. 

That  this  law  is  essentially  correct  may  be  demonstrated  by  ex- 
periment. Fig.  216  shows  the  results  from  the  series  of  tests  on 
the  McCormick  turbine,  before  mentioned,  at  full  gate.  Three  sets 

no 


100 


90 


80 


70 


60 


50 


X 


i 


A-  48ffVICTOR     CYLINDRICAL  GATE 
B- 99j"TURBINE    LOWELL  MASS 
C-  44"lMPROVED  NEW  AMERICAN 

D-  45 "SAMSON 

E-  5l"M£CORMICK  W-S-MORGAN 


25  30  35  40  45  50 

DISCHARGE  IN  CUBIC  FEET  PER  SECOND  UNDER  ONE  FOOT  HEAD 

Fig.  215. — Full  Gate  <p- Discharge  Curves  of  Various  Turbines. 


55. 


334 


Hydraulics  of  the  Turbine. 


of  experiments  are  platted  with  values  of  <£  equal  to  .35,  .65  and  .90 
and  for  heads  from  about  4.25  feet  to  7  I  feet.  Fig.  217  shows  the 
discharge  of  this  turbine  at  various  gate  openings  and  under  seven 
different  heads.  For  the  purpose  of  this  diagram  the  discharges 
under  each  head  have  been  reduced  to  the  theoretical  discharge  at 
one  foot  head  by  equation  16,  It  will  be  noted  from  both  Fig.  216 
and  Fig.  217  that  all  experiments  where  <f>  is  the  same  lie  close  to 
the  average  line,  and  that  the  departures  from  this  line  are  prob- 
ably due  to  experimental  errors.  The  results  are  sufficiently  close, 
however,  to  demonstrate  that  the  discharge  under  practical  condi- 
tions essentially  follows  the  law  above  expressed. 


// 


la. 

5  4 

d 

< 
u 


012345678 
DISCHARGE     IN    CUBIC    FEET     PER    SECOND 

Fig.  216.— The  Relations  of  Head  to  Discharge  of  a  12  "SmithrMcCormick 

Turbine. 


Discharge  or  a  Turbine  at  Fixed  Gate  Opening.  335 

161.  Power  of  a  Turbine. — The  power  which  may  be  generated 
by  any  wheel  depends  on  the  head  a/ailable,  the  quantity  of  water 
which  may  be  discharged  through  the  wheel  under  the  given  head, 
the  relative  speed  at  which  it  may  be  run,  and  the  efficiency  of 
operation.  Hence 


(35) 


q  w  h  e  _  q  h  e 

550  8.8 


Combining  equations  (30)  and  (35)  there  results 


(36 


550 


8.8 


From  equation  (36)  it  is  apparent  that  if  C,  e  and  a  are  constant 
for  any  given  turbine  and  fixed  gate  opening,  and  if  the  value  of  <f> 
remains  constant,  the  power  of  the  turbine  will  be  in  direct  propor- 
tion to  h^.  consequently 


1  0 

0.9 
« 

P0.7 
o  0.6 

i 

§  0.4 

k. 

O 

gO.3 
0.2 
O.I 

0.0 

0 

07.10  FOOT  HEAD 
O6.80 
•  6.40 
ttS.70                  »• 

AS.  20                     •• 
•  4.70                  .• 
U4.25 

k 

\ 

^H- 

N 

1 

A 

xj 

t 

^ 

V 

u 

\ 

& 

f 

o  jt* 

\o. 

V 

w 

| 

5 

\ 

^ 

£  « 

u 

^ 

jdi 

- 

Ni 

i 

o 

fe 

^  "i 

L 

^ 

.f 

\ 

I 

i 

A 

tit 

s 

• 

A 

< 

l<>^ 

« 

u 

5 

o 

; 

u  ^ 

J 

1 

. 

• 

VI 

c 

u 

u 

& 

1 

-§— 

k 

•U 

>. 

— 

— 

! 

J 

i 
<. 

) 
i 

a 

^ 

T 

-—  t 
I 

J3 

" 

i 

•  E 

o 



— 

/ 

I 

h 

i.   ". 

ft 

g 

h- 

8 

t- 

I 

£ 

uu 

-i» 

JL 

Zi 

.5                                     1.0                                     1.5                                    2.0                                _    2.  5                            2.9 

DISCHARGE   INtCUMC  FEET  PEK.tCCONO   UNDER   ONE   FOOT    HEAD 

Fig,  217. — Relations  of  Velocity  to  Discharge  for  a  12"  "Smith-McCormick' 
Turbine  at  Various  Gate  Openings. 


336 


Hydraulics  of  the  Turbine. 


U-.l 

Equation  (37)  may  be  reduced  to 


(38) 


P  = 


From  which  can  be  determined  the  power  of  a  wheel  at  any  given 
head,  provided  its  power  at  any  other  head  is  known. 
In  equation  (38)  if  h±=i,  there  results 

(39)  P  =  P1h2' 

From  which  it  may  be  stated:  In  a  given  turbine  with  a  fixed  gate 
opening,  the  power  that  can  be  developed  at  any  head  will  be  equal- 
to  the  power  at  one  foot  head  multiplied  by  h*. 

This  law  may  also  be  demonstrated  experimentally  as  will  be 
seen  by  reference  to  Fig.  218,  in  which  is  shown  the  theoretical 
curve  representing  the  relation  between  head  and  horse  power  of 
the  12"  McCormick  turbine  before  mentioned.  The  turbine  on 
which  these  experiments  were  made  was  small  and  the  heads  were 


& 


0  1.0  2.0  3.0  4.0 

ACTUAL  HOPSE   POWER   OF   WHEEL 

Fig.  218.— Relations  of  a  Power  to  Head  in  a  12  "Smith-McCormick  Turbine.' 


The  Relation  of  Discharge  to  Diameter  of  a  Turbine.       337 


limited  so  that  there  is  some  variation  from  the  theoretical  curves 
but  the  fact  expressed  by  the  general  law  is  quite  clearly  shown. 

162.  The  Relation  of  Discharge  to  the  Diameter  of  a  Turbine. 
—In  any  homogeneous  system  of  water  wheels,  the  diameter,  height 
and  corresponding  openings  and  passages  are  proportional  and  it 
follows  that  in  such  similar  wheels  similar  areas  are  proportional  to 
each  other  and  to  the  squares  of  any  lineal  dimension.  In  such 
wheels,  therefore,  the  area  a  of  the  gate  openings  is  proportional  to 
the  square  of  the  diameter  of  the  wheel,  and  the  equation  may  there- 
fore be  written : 

(40)  Cal/  2g~  =  K  D8 

In  this  equation  K  is  a  constant  to  be  determined  by  experiment. 
Combining  equations   (40)   and  (30)  there  results 

(41)  q  =  KDVF 

from  which  can  be  obtained,  by  transposition 


(42) 


Equation  (41)  is  not  only  theoretically  but  is  also  practically  cor- 
rect, as  is  shown  by  the  data  in  Table  XXVII,  which  is  also  graphi- 
cally represented  in  Fig.  219.  These  data  are  taken  from  a  paper 

TABLE  XXVII. 

Discharge  of  thirteen  water  wheels  of  the  same  manufacture  but  of  different  di- 
ameters, as  determined  by  actual  tests,  compared  with  value  computed  by  the 
formula: 

q  =  K  D2  t/h  in  which  h  =  13,  K  =  .0172 
DISCHARGE. 


No. 

Diam- 
eter in 
inches. 

Reduced 
from  actual 
tests,  Cu.  ft. 
per  Sec. 

Computed 
(  Mean 
Curve)  Cu. 
ft.  per  Sec. 

Variation 
from  Com- 
puted Dis- 
charge Cu. 
ft.  per  Sec. 

Per  cent. 
Variation 
from  Com- 
puted Dis- 
charge. 

1     . 

9 

5.17 

5.02 

+  0.15 

+  2.99 

2... 

12 

8.79 

8.92 

—0.13 

—1.46 

3  

15 

13.85 

13.93 

—0.08 

—0.57 

4  

18 

18.85 

20.07 

—1.22 

—6.08 

5  

12 

29.07 

27.32 

+  1.75 

+  6.41 

6  

24 

35.31 

35.68 

—0.37 

—1.04 

7  . 

27 

47.81 

45.16 

+  2.65 

+  5.87 

8. 

30 

54.15 

55.75 

—1.60 

—2.87 

9.  ,  

36 

77.33 

80.28 

—2.95 

-3.67 

10  

39 

93.51 

94.22 

—0.71 

-0.75 

11 

42 

107.73 

109.27 

—1.54 

—1.41 

12. 

45 

128.53 

125.44 

+  3-09 

+  3.10 

13.  - 

51 

161.07 

161  .  12 

—0.05 

0.03 

338 


Hydraulics  of  the  Turbine. 


by  A.  W.  Hunking,  entitled  "Notes  on  Water  Power  Equipment," 
in  vol.  13,  No.  4,  of  Jour.  Asso.  Eng.  Soc.,  April,  1894.  In  this  table 
are  given  the  discharges  of  thirteen  water  wheels  of  various  diam- 
eters, the  discharges  of  which  were  determined  from  actual  tests. 


DISCHARGE    IN    CUBIC    FEET    PER    SECOND 


c 

r 

3                  C 

3        i 

3-      i 

5         S 

D                    ( 
3                  t 

I          \ 

o  •  . 

3  ( 

&                    1 
3                    C 

s      i 

s      i 

3         R 

D                   C 

2  - 

1° 
n 

3  •" 

\ 

*  a 
^  u 

Vx 

1 

5SJ 

^ 

^~ 

2  a 

i. 

to 

^j 

^> 

5" 

en 

*«* 

Fig.  219. — Relations  of  Discharge  to  Diameter  in  Reaction  Turbine  of  the 

same  manufacture. 

These  results  have  been  reduced  to  the  common  basis  of  the  dis- 
charge at  13  foot  head.  The  computed  discharges  at  13  foot  head 
on  the  basis  of  equation  (41)  are  also  given,  as  well  as  the  percent- 
age of  variations  of  the  actual  from  the  theoretical  discharges.  The 
wheels  were  of  the  same  make  with  inward  and  downward  dis- 
charge. The  departures  or  variations  from  the  mean  values,  as  de- 
termined by  calculation,  are  probably  due  both  to  imperfections  in 
the  construction  of  the  wheel  and  to  errors  in  making  the  tests. 
They  may  be  seen,  however,  to  practically  conform  to  the  theoreti- 
cal deductions.  The  values  of  the  coefficient  K,  as  calculated  from 
the  tables  contained  in  the  catalogues  of  various  manufacturers  of 
American  wheels,  are  given  in  Table  XXVIII. 

163.    The  Relation  of  Power  to  the  Diameter  of  a  Turbine. — By 
substituting  the  value  of  q  from  equation  (41)  in  equation 


(35) 

there  results 
(43) 


qhe 

"    8.8 


The  Relation  of  Power  to  the  Diameter  of  a  Turbine.      339 

TABLE  XXVIII. 

Showing  Relation  of  Diameter  and  Discharge  of  Various  American  Turbines- 
working  under  Catalogue  Conditions. 

K=  WL 


Manufacturer. 


Name  of  Wheel. 


K 


Min. 


Max. 


Reaction  Wheels. 


T.  C.  Alcott  &  Son , 


Alexander,  Bradley  &  Dunn- 
ing  

American  Steel  Dredge  Wks.. 
Camden  Water  Wheel  Worki- 
Chase  Turbine  Mfg.  Co 


Christiana  Machine  Co 

Craig,  Ridgway  &  Son  Co — 
Craig,  'Ridgway  &  Son  Co — 
Dayton  Globe  Iron  Works  Co. 


J.  L.  &S.  B.  Dix 

Dubuque  Turbine  &  Rollei 
Mill  Co 

Dubuque  Turbine  &  Roller 
Mill  Co. . . 


Holyoke  Machine  Co 

Humphrey  Machine  Co 

Rodney  Hunt  Machine  Co.. 


E.  D.  Jones  &  Sons  Co . 
James  Leffel  &  Co 


Munson  Bros.  Co 

Norrish,  Burn  ham  &  Co. 
Platt  Iron  Works  Co 


Alcott' s  Standard  High  Duty 
Alcott' s  Special  High  Duty. 


*Syracuse  Turbine 

*  Little  Giant 

United  States  Turbine 

*Chase-Jonval  Turbine  (reg- 
ular)  

*Chase-Jonval  Turbine 
(special) 

Balanced  Gate  Turbine 

Double  Perfection 

Standard 

*American  Turbine 

New  American  (high   head 
type) 

Improved  New  American.. 

Special  New  American 

Improved  Jonval  Turbine. . 


Flenniken  Turbine. 


McCormick's  Holyoke  Tur 
bine 

Hercules  Turbine 

flXL  Turbine 

fXLCR  Turbine 

McCormick's  Holyoke  Tur- 
bine  

*Hunt-McCormick  Turbine. 

New  Pattern  Hunt  Turbine. 

Standard  Wheel,  1887  pat- 
tern   

Crocker  Wheel 

Samson 

Improved  Samson 

Standard 

Special 

J  Phoenix  "Little  Giant"  . . . 


Victor  Register  Gate ....'. 

Victor  Standard  Cylinder 

Gate 


.00654 
.0157 

.00538 

.0205 

.0214 


.01086 

.00902 

.0116 

.00586 

.00543 

.00509 
.0233 
.0175 
.00454 

.00652 


.0184 
.0162 
.00351 
.00645 

.01877 
.01913 
.01297 

.0123 

.0175 

.0170 

.022 

.00612 

.00937 

.00924 

.00917 

.0167 

.0222 


-00860 
.0168 

.00622 

.0340 

.0229 

.00913, 

.01346 

.00952: 

.0142 

.00659- 

.00801 

.00644- 
.0263 
.0205 
.00546- 

.0088 


.0191 
.0175 
.00536 
.00953 

.01929 
.02867 
.01543 

.0141 

.0179 

.0171 

.022 

.00640* 

.00965 

.0172 

.00955- 

.0186 

.0227 


340 


Hydraulics  of  the  Turbine. 


TABLE  XXVIII.— Continued. 

Showing  Relation  of  Diameter  and  Discharge  of  Various  American  Turbines 
working  under  Catalogue  Conditions. 

-      q 


K 

Manufacturer. 

Name  of  Wheel. 

Min. 

Max. 

Reaction  Wieels.—CoTi. 

Poole  Engineering  and  Ma- 
chine Co          

Poole-Leffel  .... 

.00625 

.00827 

T.  H   Risdon  &  Co  

*Risdon  Standard  Turbine  .  . 

.00501 

.00698 

-'S.  Morgan  Smith  Co  

*Risdon  Type  T.  C.  Turbine 
*Risdon  Type  D.  C.  Turbine 
*Smith-McCormick 

.00753 
.0100 
0187 

.00948 
.0132 
0238 

Smith             .  .         ... 

0247 

.0256 

Trump  Mfg   Co  .  . 

Standard  Trump 

0210 

0263 

Wellman,  Seaver,  Morgan  Co. 

McCormick  

.0185 

.0199 

Impulse  Wheels. 
DeRemer  Water  Wheel  Co.  . 
Abner  Doble  Co 

*DeRemer  Water  Wheel.  . 
*Tangential  Wheel 

.000135 
000075 

.000173 
000119 

Pelton  Water  Wheel  Co.  . 

^Tangential  Wheel. 

00010 

000135 

Platt  Iron  Works  Co  

Victor  High  Pressure  ...    . 

0170 

0''*47 

Risdon  Iron  Works  

*Tangential  Wheel  

000134 

000173 

*Wide  variation  in  constants  due  to  the  design  being  special  for  various  sized  wheels  (series 
not  exactly  homogeneous). 

tTables  in  catalogue  based  on  full  theoretical  power  of  the  water.  Wheels  are  said  to  give  from 
75  per  cent  to  90  per  cent  efficiency,  depending  on  location. 

$Munson  Bros.  Co.  make  several  types  of  "Litte  Giant"  turbines  causing  above  wide  variation  in 
-constants. 


-  is  constant  for  a  given  wheel,  as  long  as  <f>  is  constant, 
this  expression  may  be  represented  by  a  constant  K2  which  may 
1^e  derived  independently  for  each  make  of  wheel,  or  may  be  deter- 
mined from  the  equation 


(44) 


K    -Ke 

K~ 


With  this  substitution   (43)  becomes 
(45)  p  rr  K2D2h* 

That  is  to  say:  With  wheels  of  homogeneous  design,  the  power  of 
any  wheel  under  the  given  head  is  in  direct  proportion  to  the  square 
-of  its  diameter.  This  law  is  both  theoretically  and  practically  cor- 
rect, as  demonstrated  by  Table  XXIX,  and  Fig.  220,  taken  from  the 
paper  by  Mr.  Hunking  to  which  reference  has  previously  been 


Relation  of  Speed  to  Discharge  of  Turbine. 


34* 


TABLE  XXIX. 

Horse  Power  of  thirteen  water  wheels  of  the  same  manufacture  but  of  different 
diameters,  as  determined  by  actual  tests,  compared  with  values  determined 
by  the  formula: 

P=K2  D2  h1 


K2 =.00158 
HORSE  POWER 


h  =  13 


No. 

Diame- 
ter in 
inches. 

From  Tests. 

Computed. 

Variation 
from  Com- 
puted H.  P. 
in  H.  P. 

Variation 
from  Com- 
puted H.  P. 
Percent. 

1.  

9 

6  10 

6  00 

+  0  10 

+  1.67 

2  

12 

1041 

1067 

—026 

—2.44 

3  

15 

16  49 

1667 

—018 

—1.08- 

4  

18 

22  89 

24  00 

—1.11 

—4.62- 

5  

21 

33  71 

32.67 

+  1.04 

+  3.18 

6  

24 

41.53 

42.67 

—1.14 

—2.67 

7 

27 

56  67 

54  07 

+  2  60 

+  4.81 

8  

30 

63  69 

66  68 

—299 

-4.48 

9  

36 

97  45 

9600 

+  1.45 

+  1.50 

10  

39 

10998 

112  68 

—2.70 

—2.40 

11  

42 

13309 

13069 

+  2.40 

+  1.84 

12  

45 

15382 

150.02 

+  3.80 

+  2.53 

13  

51 

196  28 

192.69 

+  3.59 

+  1.86 

Fig.  220. — Relation  of  Power  to  Diameter  in  Reaction  Turbines  of  the  same 

manufacture. 


342 


Hydraulics  of  the  Turbine. 


made.  This  table  and  figure  illustrate  the  relation  between  the  the- 
oretical power,  as  determined  by  equation  (45),  and  the  actual  horse 
power  of  thirteen  wheels  of  the  same  manufacture  but  different 
diameters,  as  determined  by  actual  tests. 

The  values  of  the  constant  K2  for  the  most  efficient  relation  of 
power  to  diameter  in  various  American  turbines,  as  calculated  from 
the  tables  contained  in  the  catalogues  of  various  American  manu- 
facturers of  turbines,  are  given  in  Table  XXX.  The  values  of  K2 
and  other  turbine  constants  will  be  found  to  vary  widely  in  the 
various  types  of  turbines,  not  only  of  different  manufacturers  but 
of  the  same  manufacturer.  The  interpretation  of  this  fact  is  not 
that  one  turbine  is,  in  the  abstract  and  according  to  the  relative 
value  of  the  constants,  more  valuable  than  another,  but  that  each 
turbine  is  best  fitted  for  a  particular  range  of  conditions  for  which 
it  was  presumably  designed. 

TABLE  XXX. 

Showing  Halation  of  Power  and  Diameter  of  Various  American   Turbines  Work 
ing  under  Catalogue  Conditions. 

K°  ="~ 


Manufacturer. 


Name  of  Wheel. 


K. 


Min. 


Max. 


Reaction  Wheels. 


T.  C.  Alcott  &  Son, 


Alexander,  Bradley  &  Dunn- 
ing  

American  Steel  Dredge  Wks. 
Camden  Water  Wheel  Works 
Chase  Turbine  Mfg.  Co 


Christiana  Machine  Co 

Craig,  Ridgway  &  Son  Co 

Craig,  Ridgway  &  Son  Co 

Dayton  Globe  Iron  Works  Co. 


J.  L.  &S.  B.  Dix 

Dubuque    Turbine  &  Roller 
Mill  Co 

Dubuque    Turbine   &   Roller 
Mill  Co.. 


Alcott' s  Standard  High  Duty 
Alcott's  Special  High  Duty. 


Syracuse  Turbine 

Little  Giant 

United  States  Turbine. . . . 

*Chase-Jonval  Turbine  (reg- 
ular)   

*Chase-Jonval  Turbine 
(special) 

Balanced  Gate  Turbine 

Double  Perfection 

Standard 

*  American  Turbine 

*New  American  (high  head 
type) 

Improved  New  American. . . 

Special  New  American 

Improved  Jonval  Turbine. . 

Flenniken  Turbine 

McCormick's  Hoi  yoke  Tur- 
bine.. 


.000589 
.00141 

.000483 

.00190 

.00190 

.000590 

.000932 

.000800 

.00113 

.000538 

.000434 

.000422 
.00212 
.00158 
.000447 

.000596 


.00167 


.000999 
.00155 

.000565 

.00332 

.00207 

.000780 

.001150 

.000854 

.00120 

.000629 

.000726 

.000588 
.00244 
.00187 
.000532 

.000802 


.00173 


The  Relation  of  Power  to  the  Diameter  of  a  Turbine.     343 


TABLE  XXX.— Continued. 

Showing  Relation  of  Power  and  Diameter  of  Various  American  Turbines  Work- 
ing under  Catalogue  Conditions. 


* 

^2 

Manufacturer. 

JSame  of  Wheel. 

Min. 

Max. 

Reaction  Wheel.  —  Con. 
Holyoke  Machine  Co  

Hercules  Turbine  

00147 

001  ^Q 

Humphrey  Machine  Co  

|IXL  Turbine 

0003Q7 

OOfkrtOft 

fXLCR  Turbine  

000730 

001  31  0 

Rodney  Hunt  Machine  Co.  .  . 

McCormick    Holyoke    Tur- 
bine   

00169 

00173 

*Hunt  McCormick  Turbine. 
New  Pattern  Hunt  Turbine 
Standard  Wheel,  1887  Pat- 
tern .  .  :  

.00173 
.00120 

00101 

.00260 
.00146 

00122 

E.  D.  Jones  &  Sons  Co  

Crocker  Wheel 

00159 

00163 

James  Leffel  &  Co  

Samson  . 

00158 

00159 

Improved  Samson 

00201 

00202 

Standard  

00056 

00058 

Special  

000897 

000920 

JPhoenix  "Little  Giant" 

000842 

001  560 

000852 

000885 

Platt  Iron  Works  Co  

Victor  Re^i^ter  Gate 

00158 

00179 

Victor   Standard     Cylinder 
Gate  

00205 

00205 

Poole  Engineering  and  Ma- 
chine Co.  

Poole-Leffel 

000625 

000650 

T.  H.  Risdon  &  Co  

*Risdon  Standard  Turbine. 

000485 

000675 

S.  Morgan  Smith  Co. 

*Risdon  Type  T.  C.  Turbine 
*Risdon  Type  D.  C.  Turbine 
Sinith-McCormick 

.000672 
.000781 
00169 

.000913 
.00135 
00217 

Smith 

00232 

00236 

The  Trump  Mfg.  Co  

Standard  Trump  

00191 

00241 

Wellman,  Seaver,  Morgan  Co. 

.00168 

.00171 

Impulse  Wheels. 

DeRemer  Water  Wheel  Co.. 
Abner  Doble  Co  .       .      . 

*DeRemer  Water  Wheel  .  .  . 
*Tanwential  Wheel 

.000124 
0000055 

.000186 
0000107 

Pelton  Water  Wheel  Co  
Platt  Iron  Works  Co 

^Tangential  Wheel  

.0000093 
00154 

.0000130 
00^23 

Risdon  Iron  Works  Co 

*Tangential  Wheel 

0000128 

0000165 

*Wide  variation  in  constants  due  to  the  design  being  special  for  various  sized  wheels  (series  not 
exactly  homogeneous). 

tTables  based  on  full  theoretical  power  of  the  water.  Wheels  are  said  to  give  from  75  per  cent 
to  90  per  cent  efficiency,  depending  on  location. 

fcMunson  Bros.  Co.  make  several  types  of  "Little  Giant"  turbines,  causing  above  wide  variation 
in  constants. 


344 


Hydraulics  of  the  Turbine. 


C"J 


CM 


c 

LJ 

H 
O 
0 


01 


\ 


CD 


V 


VN 

X 


^^ 


\ 


CO 


CNJ 


^ 


"*-.. 


\ 


\\ 


CD 
10 


in 


a 
m 


CM 


S3HONI      HI     133HM     JO 


Relation  of  Speed  to  Discharge  of  Turbine.  345 

As  the  power  of  a  wheel  varies  directly  with  the  value  of  K2,  this 
constant  is  a  direct  measure  of  comparative  power  and  indicates 
the  relative  power  that  can  be  developed  by  various  types  of  wheels 
of  the  diameter  and  under  a  given  head.  The  range  of  values  for 
K2  as  found  in  American  practice  is  shown  graphically  in  Fig.  221 
where  the  power  of  turbines  of  various  diameter  and  types  under 
one  foot  head  is  given.  The  power  of  a  wheel  varies  under  differ- 
ent heads  as  h^,  and  therefore  the  power  at  any  head  can  be  de- 
termined directly  by  multiplying  the  readings  of  the  graphical  table 
by  h*.  For  example,  from  Fig.  221  it  will  be  seen  that  various 
types  of  40"  American  wheels,  under  one  foot  head,  will  give  from 
.75  to  4  H.  P.  and  at  16  foot  head  they  will  therefore  develop  64 
times  the  H.  P.  at  one  foot  head  or  from  48  to  256  H.  P.  within 
which  range  a  choice  must  be  made. 

164.  Relations  of  Speed  to  Discharge  of  Turbines. — As  the  speed 
of  all  wheels  of  the  same  series  must  be  proportional  to  Vh>  the 
equation  may  be  written : 

(46)  v'  =   K.T/F 

from  which  and  from  equations   (19)   and   (21) 


(47)  K3  -  _  -  r   „  ^        12  x 
From  equations  (42)   and  (47)   may  be  derived 

(48)  n  =  H 


As  the  first  term  of  the  last  expression  is  constant,  there  may  be 
written : 


(49)  K4  = 


12X60  K3K 


from  which  equation  (48)  may  be  re-written. 

K^W 

(50)  n  =  - 

A 

'For  a  head  of  one  foot,  h=i,  equation  (50)  becomes 

(51)  n    -r-L 


Equation  (50)  may  be  rearranged  to  read: 

(52)  K4  =  -lL|/^=  =  n 

21 


346 


Hydraulics  of  the  Turbine. 


TABLE  XXXI. 

Showing   Relation   of  Speed   and   Discharge  of   Various   American    Turbines 
Working  under  Catalogue  Conditions. 


I 

^4 

Manufacturer. 

Name  of  Wheel. 

Min. 

Max. 

Reaction  Wheels. 
T.  C.  Alcott  &  Son 

Alexander,  Bradley  &  Dunn- 
ing. . 

Alcott's  Standard  High  Duty 
Alcott'  s  Special  High  Duty. 

98.8 
154.5 

114.7 
159.2 

American  Steel  Dredge  Wrks. 

^Syracuse  Turbine  
*Littie  Giant  

89.8 
172  0 

108  .  2 
943  8 

Camden  Water  Wheel  Works 
Chase  Turbine  Mfg.  Co  

United  .States  Turbine  

205.2 

239.2 

*  Chase  Jon  val  Turbine  (reg- 
ular) . 

140  0 

174  0 

*Chase-Jonval  Turbine 
(special) 

901  0 

255  0 

Christiana  Machine  Co 

Balanced  Gate  Turbine  .  . 

115  8 

126  2 

Craig,  Ridgway  &  Son  Co  

Double  Perfection  

90  5 

97  2 

Craig,  Ridgway  &  Son  Co  

Standard 

94  0 

101  2 

Dayton  Globe  Iron  Works  Co. 

^American  Turbine.  .  .  .  . 

83.0- 

109  0 

fNevv  American  (high  head 
type)  .  . 

75  4 

85  9 

J.  L.  &  S.  B.  Dix.  . 

Improved  New  American.  .  . 
Special  New  American  

265.0 
170.5 

ft_t   A 

268.0 
190.0 
i  on  n 

Dubuque  Turbine  &    Roller 
Mill  Co  

mn 

1  C£>     A 

Dubuque  Turbine  &    Roller 
Mill  Co  

IVTnr^rkrmipb-'fi    T^nlvrifca    Tii  r 

bine  

IP)'?    0 

176  0 

Holvoke  Machine  Co  

148  0 

154  0 

Humphrey  Macnine  Co  

1IXL  Turbine 

71  3 

88  3 

JXLCR  Turbine.  . 

90  5 

116  9 

Rodney  Hunt  Machine  Co.  .  . 

McCormick's  Holvoke  Tur- 
bine.    

159  5 

176.0 

*Hunt  McCormick  Turbine. 
*New  Pattern  Hunt  Turbine 
Standard  Wheel,   1J»87   Tat- 
tern 

161.4 
132.4 

19(3  o 

207.5 
174.8 

145  0 

E.  D.  Jones  &  Sons  Co  

Crocker  Wheel 

161  0 

169  8 

James  Leffel  &  Co  

9n  i  7 

9/VJ     A 

Improved  Sampson  

240  0 

241.5 

Standard 

]03  7 

107  0 

Special 

134  7 

139.8 

Munson  Bros.  &  Co  
Norrish,  Burnham  &  Co.  ... 

tJPhoenix  -'Little  Giant" 

102.0 
1  15  .  9 

132.1 
120.0 

Platt  Iron  Works  Co  

V               T?        '    f          C"     f 

1  Y3  0 

Wo 

Victor    Standard     Cylindei 
Gate  .  . 

205.0 

2:2.0 

Relation  of  Speed  to  Power  of  Turbine. 


347 


TABLE  XXXI.— Continued 

Showing    Relation  of  Speed   and  Discharge  of   Various   American   Turbines 
Working  under  Catalogue  Conditions, 


L 

"-4 

Manufacturer. 

JName  of  Wheel. 

Mm. 

Max. 

Reaction  Wheels.  —  Con. 

Poole  Engineering  and  Ma- 
chine Co  .           . 

Poole-Leffel 

1104 

me 

T  H   Risdon  &  Co 

*Risdon  Standard  Turbine 

QQ    4 

mo 

S.  Morgan  Smith  Co  

*Risdon  Type  T.  C.  Turbine 
*Risdon  Type  D.  C.  Turbine 
Smith-McCormick  

100.7 
108.0 
163  7 

137.3 
158.0 
185  0 

Smith  

265  0 

266  0 

The  Trump  Mfg.  Co  

Standard  Trump 

194  0 

in  o 

Well  man,  Seaver,  Morgan  Co. 

McCormick  

168.5 

179  0 

Impulse  Wheels. 
DeRemer  Water  Wheel  Co.  . 

DeRemer  Water  Wheel.  .  .  . 

11  10 

13  20 

Abner  Doble  Co  

^Tangential  Wheel 

6  61 

9  20 

Pelton  Water  Wheel  Co  

Tangential  Wheel 

9  21 

10  92 

Platt  Iron  Works  Co 

Victor  High  Pressure 

37  8 

42  2 

Risdon  Iron  Works  

Tangential  Wheel 

10  67 

12  10 

*Wide  variation  in  constants  due  to  the  design  being  special  for  various  sized  wheels  (series  not 
exactly  homogeneous). 

tUatalogue  recommends  a  maximum  and  minimum  speed.  Constants  given  are  for  the  average 
speed. 

^Tables  in  catalogue  based  on  full  theoretical  power  of  the  water.  Wheels  are  said  to  give  from 
75  per  cent  to  90  per  cent  efficiency,  depending  on  location. 

$$Munson  Bros.  Co.  make  several  types  of  "Little  Giant"  turbines  causing  above  wide  variation 
in  constants. 


It  is  evident  that  K4  is  constant  for  all  turbines  with  constant  K 
and  K3 ;  also,  for  all  turbines  where  q,  the  discharge,  is  equal  at  the 
same  speed,  n,  and  under  the  same  head,  h,  K4  must  be  constant  for 
different  heads  since  n  and  q  are  proportional  to  Vn-  The  values  of 
the  constant  K4  as  calculated  from  the  tables  contained  in  the 
catalogues  of  various  American  manufacturers  are  given  in  Table 
XXXI. 

i64a.  Relation  of  Speed  to  Power  of  Turbines. — From  equation 
(35)  may  be  derived 

8.8  P 


(53) 


eh 


348  Hydraulics  of  the  Turbine. 

From  equation  (48)  may  be  derived 


•(«*)  K,  !/K   =  12  X  «u  X  Vh   *    7? 

Combining  equations  (53)  and  (54) 


(55) 


12  X  60l/e 
By  transposing 

K.T/K   12X60     nr  = 


(56) 

As  the  first  member  of  the  equation  is  constant  for  any  given 
wh ®el,  there  may  be  written 

(57) 
and  hence 

(58)  K<      n"^ 

From  equation  (58)  it  will  be  noted  that  the  value  of  K5  under  a 
given  head  is  in  direct  proportion  to  the  square  of  the  velocity  of 
the  wheel  and  to  its  power.  K5  is  termed  the  "specific  speed"  of  the 
wheel.  A  high  value  of  K5  is  an  indication  of  high  speed,  and  a 
low  value,  of  low  speed. 

The  values  of  the  constant  K5  as  calculated  from  the  tables  con- 
tained in  the  catalogues  of  various  manufacturers  of  American 
wheels  are  given  in  Table  XXXII. 

Fig.  2-22  shows  graphically  the  relation  of  power  to  speed  under 
one  foot  head,  as  expressed  by  the  constant  K5  within  the  range  of 
practice  of  American  turbine  builders. 

The  use  of  the  diagram  may  be  illustrated  as  follows : — 

At  35  revolutions  per  minute  various  types  of  American  wheels 
will  develop  from  I  to  5.8  horse  power.  For  the  best  efficiency, 
that  is  for  a  constant  value  of  <£,  the  number  of  revolutions  ot  a 

wheel  will  vary  as  i/h,  and  the  power  will  vary  as  h*.  Thus  for 
a  1 6  foot  head  these  wheels  will  run  four  times  as  fast  as  for  a  one 
foot  head  or  at  140  R.  P.  M.,  and  will  develop  64  times  the  power 
that  will  be  developed  at  a  one  foot  head,  or  from  64  to  371  H.  P., 
between  which  limits  the  wheel  must  be  chosen. 

Suppose  a  wheel  is  desired  to  develop  500  H.  P.  at  150  R.  P.  M. 
under  25  foot  head.  These  conditions  correspond  to  4  H.  P.  at  30 


Relation  of  Speed  to  Power  of  Turbine. 


349 


3 4 5  6~~ 8  8          10          II 

HORSE  POWER    UMDEfl   ONE   FOOT   HEAD. 

Fig.  222. — Speed  Curves  of  Various  Standard  American  Wheels. 


350 


Hydraulics  of  the  Turbine. 


TABLE  XXXII. 

Showing  Relation  of  Speed  and  Power  of  Various  American  Turbines  working 
under  Catalogue  Conditions. 


1 

^5 

Manufacturer. 

Name  of  Wheel. 

Min. 

Max. 

Reaction  Wheels. 
T.  C.  Alcott  &  Son  

Alcott'  s  Standard  High  Duty 

941 

1216 

Alexander,  Bradley  &  Dunn- 
iner.  . 

Alcott's  Special  High  Duty. 

2152 
723 

2300 
830 

American  Steel  Dredge  \Vrks 

^Little  Giant 

2880 

5420 

Camden  Water  Wheel  Works 
Chase  Turbine  Mfg  Co 

United  States  Turbine  
*Chase-Jonval  Turbine  (  reg- 

3780 

4570 

ular  ^  

1680 

2580 

*Chase-Jonval    Turbine 
(special  )  

3460 

5530 

Christiana  Machine  Co 

Balanced  Gate  Turbine 

1220 

1475 

Craig,  Ridgway  &  Son  Co 

Double  Perfection  . 

840 

895 

Craig,  Ridgwav  &  Son  Co 

Standard                    .   ... 

776 

975 

Dayton  Globe  Iron  Works  Co 

*American  Turbine.   .    . 

623 

1140 

fNew  American  (high  head 
type)  

520  " 

674 

J.  L.  &S.  B.  Dix  . 

Improved  New  American  .  . 
Special  New  American  
Improved  Jonval  Turbine 

6100 
2490 
965 

.    6477 
3293 
1363 

Dubuque  Turbine    &  Roller 
Mill  Co.   . 

Flenniken  Turbine 

1350 

1880 

Dubuque  Turbine  &    Rollei 
Mill  Co  

McCormick's  Holyoke  Tur- 

bine .  .             

2380 

2810 

Holyoke  Machine  Co  

Hercules  Turbine  

2030 

2155 

Humphrey  Machine  Co  . 

JIXL  Turbine. 

572 

889 

JXLCR  Turbine 

1052 

1545 

Rodney  Hunt  Machine  Co.  . 

McCormick's  Holyoke  Tur- 
bine   

2310 

2810 

*Hunt  McCormick  Turbine. 
*New  Pattern  Hunt  Turbine 
*>'tandaid  Wheel,  1887  Pat- 
tern    

2360 
1624 

1665 

3910 
2900 

2160 

E.  D.  Jones  &  Sons  Co 

2360 

2680 

James  Leffel  &  Co  

Samson  

3775 

3833 

Improved  Samson  
Standard  

5013 
948 

5400 
1063 

Special  

1730 

1858 

Munson  Bros.  &  Co 

JJPhoenix  "Little  Giant" 

843 

1600 

Norrish,  Burnharn  &  Co.  .   . 

1130 

1345 

Platt  Iron  Works  Co  

Victor  Register  Gate  

2254 

2712 

Victor  Standard  Cylinder 
Gate 

3733 

4145 

Victor  High  Pressure  

129  10 

169.50 

Relation  of  Speed  to  Power  of  Turbine. 


TABLE  XXXII.— Continued. 

Showing  Relation  of  Speed  oni  Power  of  Various  American  Turbines  working 
under  Catalogue  Conditions. 


] 

*. 

Manufacturer. 

Name  of  Wheel. 

Min. 

Max. 

Reaction  Wheels.—  Con. 

TJoole  Engineering  and  Ma- 
chine Co 

Poole-Leffel  

1170 

1239 

T  H   Risdon  &  Co 

*Risdon  Standard  Turbine 

2351 

3680 

8  Morgan  Smith  Co  

*Ri.-don  Type  T.  C.  Turbine 
*  Risdon  Tvpe  D.  C.  Turb.ne 
Smith  McCormick  

3520 
46UO 
2640 

5070 
7370 
3013 

Smith  

6165 

6640 

The  Trump  Mfg  Co 

Standard  Trump 

;•#  07 

4250 

Wellman,  Seaver,  Morgan  Co. 

2380 

2862 

Impulse  Wheels. 

DeRemer  Water  Wheel  Co.  . 
Abnei'  Doble  Co         

*DeRemer  Water  Wheel.  .  .  . 
^Tangential  Wheel     

12.34 
4.00 

18.01 

7  62 

Pelton  Water  Wheel  Co  

^•Tangential  Wheel  

7.84 

11.42 

Risdon  Iron  Works  

*Tangential  Wheel  

8.24 

11.22 

*Wide  variation  in  constants  due  to  the  design  being  special  for  various  sized  wheels  (series  not 
exactly  homogeneous). 

tCatalogue  recommends  a  maximum  and  minimum  speed.  Constants  given  are  for  the  average 
speed. 

^Tables  in  catalogue  based  on  full  theoretical  power  of  the  water.  Wheels  are  said  to  give  from 
75  per  cent  to  90  per  cent  efficiency,  depending  on  location. 

ft.Munsoti  Bros.  Co.  make  several  types  of  "Little  Giant"  turbines  causing  above  wide  variation 
in  constants. 

R.  P.  M.  under  one  foot  head,  and  would  require  a  wheel  having  a 
constant  K5  =  36oo. 

165.  Value  of  Turbine  Constants. — The  values  of  the  constants 
discussed  in  this  chapter  have  been  determined  fro-m  the  cata- 
logues of  the  manufacturers  of  American  turbines  and  are  the  values 
which  may  be  used  for  determining  the  manufacturer's  standard  re- 
lations of  the  wheel  for  particular  and  fixed  conditions  where  <£  is 
constant,  as,  for  example,  the  development  of  a  certain  power  under 
a  fixed  head  and  with  a  given  speed.  When  the  head  varies  at  dif- 
ferent times,  the  value  of  <j>  also  varies  and  the  value  of  the  other  co- 
efficients of  the  turbine,  A,  K,  K2,  K4,  and  K5,  will  also  vary.  In 
order  to  discuss  such  conditions  the  laws  of  the  variations  of  these 
constants,  for  any  series  of  wheels,  must  be  known.  These  laws 


352  Hydraulics  of  the  Turbine. 

can  be  ascertained  from  a  complete  test  of  any  one  wheel  of  the 
series  and  the  laws  so  determined  will  hold  for  the  entire  series  if 
the  series  is  actually  constructed  on  homogeneous  lines.  Owing  to 
imperfections  in  the  processes  of  manufacture,  there  is  actually 
more  or  less  variation  between  different  wheels  of  a  series.  It  is 
therefore  desirable,  when  the  approximate  size  of  the  wheel  needed 
is  known,  to  secure  a  test  of  a  wheel  of  that  particular  size  and 
hand. 

Of  the  constants  discussed,  <£  and  A  express  the  standard  rela- 
tion recommended  by  the  manufacturer  between  diameter  and  speed 
in  the  series  of  wheels  he  offers.  See  equations 

(23)  n 


(24) 

ii 

The  coefficient  K  is  the  constant  of  discharge  and  shows  the 
standard  relation  for  various  types  of  turbines  between  the  quantity 
of  water  discharged  and  the  diameter  of  the  wheel.  See  equations 

(41)  q  = 

(42)  D  = 

K2  is  the  constant  of  power  and  shows  the  standard  relation  be- 
tween the  diameter  of  the  wheel  and  the  power.  See  equation 

(45)  P  =  K2D2h* 

K4  is  the  constant  of  discharge  and  shows  the  standard  relation 
between  speed  and  discharge.  See  equation 


(30)  n  -  I 

q 

K5  is  the  constant  expressing  the  standard  relation  of  power  and 
speed  for  a  particular  series  of  wheels.  See  equation. 

(58)  P  =  K5  1^1 

The  catalogue  tables  of  turbines  from  which  the  standard  values 
of  the  constants  in  the  preceding  tables  have  been  calculated  are 
presumably  based  on  the  actual  tests  of  certain  wheels  of  the  series. 
The  actual  results  of  a  test  of  any  individual  wheel  of  the  series  is 
likely  to  depart  to  an  extent  from  the  tabular  value.  Differences 


Literature. 


353 


will  often  be  found  between  wheels  of  different  diameters,  between 
wheels  of  the  same  diameter  but  of  opposite  hand,  and  even  between 
wheels  of  the  same  size  and  hand  which  are  supposed  to  be  con- 
structed on  identical  lines. 

These  differences  in  results  are  due  to  carelessness  in  construc- 
tion, or  to  unusually  good  construction  in  the  effort  to  secure  special 
results,  where  the  conditions  warrant  special  effort.  Any  change  in 
the  design  of  a  wheel  for  the  purpose  of  reducing  or  increasing  the 
discharge,  and  hence  reducing  or  increasing  its  power,  will  give 
rise  to  differences  in  these  coefficients  which  must  be  taken  into 
account  in  any  calculations  made  thereon.  A  careful  study  of  these 
coefficients  as  determined  from  the  actual  tests  of  any  wheel,  to- 
gether with  a  study  of  the  design  of  the  wheel  itself,  will  form  the 
basis  of  a  complete  and  systematic  knowledge  of  water  wheel  de- 
sign. 

LITERATURE. 

1.  Hermann,  Gustav.     Die  graphische  Theorie   der  Turbinen  and  Kreisel- 

pumpen.      Verhaldung  des  Vereines  zur  Beforderung  des  Gewerb- 
feisses  in  Preussen.     1884,  pp.  307-379;  521-580. 

2.  Arnot,  C.     Graphic  Turbine  Tables.     Showing  relation  of  head  and  dis- 

charge for  various  sizes  of  turbines.     Zeitschr.  d  ver  Deutsch. 
Ing.  p.  980.     1890. 

3.  Ludewig,    H.     Allgemeine    Theorie    der    Turbinen.     Berlin.     L.     Simon, 

1890. 

4.  Richards,  John.     Turbines  Compared  with  Water  Wheels.     Eng.  News. 

Vol.  1,  p.  530.    1892. 

5.  Hunking,  A.  W.     Notes  on  Water  Power  Equipment.     Jour.  Asso.  Eng. 

Soc.    Vol.  13,  p.  197.     1894. 

6.  Moissner,  G.    Die  Hydraulik  und  die  hydraulischen  Motoren.    Jena.   1895. 

7.  Bodmer,  G.  R.     Hydraulic  Motors,  Turbines  and  Pressure  Engines.     New 

York.     Van  Nostrand.     1895. 

8.  Elaine,  R.  G.     Hydraulic  Machinery.     New  York.     Spon  &  Chamberlain. 

1897. 

9.  Heines,   Charles   N.      Centrifugal    Pumps,    Turbines   and   Water   Motors. 

Manchester,  Eng.,  Technical  Pub.  Co.     1898. 

10.  Fox,  William.     Graphics  of  Water  Wheels.     Stevens  Indicator.     Vol.  16, 

p.  30.    1899. 

11.  Brauer,  Ernst  A.     Grundriss  der  Turbinen  Theorie.    Leipsig,  S.  Hirzel. 

1899. 

12.  Zeuner,  Gustav.     Vorlesungen  iiber  Theorie  der  Turbinen  mit  vorbereiten- 

den    untersuchungen    aus    der    technischen    hydraulik.     Leipsig. 
Arthur  Felix.    1899. 

13.  Rateau,  A.     Traite  des  turo-machines.    Paris.     Ch.  Dunod.     1900. 


354  Hydraulics  of  the  Turbine. 

14.  Henrotte,  J.     Turbines-hydrauliques,  pornpes  et  ventilateurs,  centrifuges,. 

princeps  theoriques,  dispositions  pratiques  et  calcul  des  dimen- 
sions.   Liege,  Imprimerie  Liegeoise.    1900. 

15.  Marks,  G.  Croiden.    Hydraulic  Power  and  Engineering.    New  York.    Van 

Nostrand.    1900. 

16.  Wood,  DeVolson.    Turbines,  Theoretical  and  Practical.    New  York.    Wiley 

&  Sons.    1901. 

17.  Miiller,  Wilhelm.     Die  Francis-Turbinen.     Hanover,  Janecke.     1901. 

18.  Kessler,  Jos.     Berechnung  and  Konstruktion  der  Turbinen.     Leipsig.     J. 

M.  Gebhardt.     1902. 

19.  Camerer,   R.      Diagrams   of   Theory   of    Turbines.      Graphic   Representa- 

tion of  Equation  with  Proof  and  Application.     Dingler's  Poly- 
tech.  Jour.  p.  693.     1902. 

20.  Thurso,  John  Wolf.     Modern  Turbine  Practice  and  the  Development  of 

Water  Power.     Eng.  News.     Dec.  4,  1902. 

21.  Rea,    Alex.      Turbines    and    the    Effective    Utilization    of    Water-Power. 

Mech.  Engr.    March  22,  1902. 

22.  Osterlin,  Hermann.     Untersuchungen  iiber  den  Energieverlust  des  Was- 

sers  in  Turbinenkanalen.     Berlin.     Julius  Springer.     1903. 

23.  Thurso,  John  Wolf.     Effect  of  Draft  Tube.     Eng.  News.     Vol.  1,   p.   29. 

1903. 

24.  de  Graffigny,  Henri.    Les  Turbo-moteurs  et  les  Machines  Rotatives.    Paris 

E.  Bernard.     1904. 

25.  Dickl,   Ignaz.  Die  Berechnung  der  achsialen  Actionsturbinen  auf  zeich- 

nerischem  Wege.  Vienna.     Spielhagen  &  Schurich.     1904. 

26.  Danckwerts.     Die  Grundlagen  der  Turbinenberechung  fur  Pratiker  and 

Studierende  des  Bauingenieurfaches.     Wiesbaden.     C.  W.  Krei- 
del.     1904. 

27.  Thurso,  John  Wolf.     Modern  Turbine  Practice.     New  York.     Van  Nos- 

trand.   1905. 

28.  Church,  Irving  P.     Hydraulic  Motors.     New  York.     Wiley  &  Sons.     1905. 

29.  Basshnus,    N.     Klassifikation    von    Turbinen.    Zeitschritt    der    Verenier 

Deutschjer  Ingenie  for  1905,  p.  922. 

30.  Graf,   Otto.     Theorie,   Berechnung  und   Konstruktion   der   Turbinen   und 

deren     Regulatoren;      ein     Lehrbuch     fur     schule     und     praxis. 
Munich.    August  Lachner.    1904  and  1906. 

31.  Wagenbach,  Wilhelm.     Neuere  Turbinenanlagen.     Berlin.     1905. 

32.  Gelpke,     Viktor.       Turbinen     und     Turbinenanlagen.       Berlin.       Julius; 

Springer.  1906. 

33.  Pfarr,    A.       Die    Turbinen    fur    Wasserkraftbetrieb.       Berlin.       Julius 

Springer.     1907. 

34.  Tangential  Water  Wheel  Buckets.     The  Engr.     May  1,  1904. 

35.  Kingsford,  R.  T.     A  Complete  Theory  of  Impulse  Water  Wheels  and  Its- 

Application  to  Their  Design.    Eng.  News.    July  21,  1898. 


CHAPTER  XV. 

TURBINE  TESTING. 

166.  The  Importance  of  Testing  Machinery. — A  correct  theory 
based  on  mathematical  analysis  forms  a  valuable  foundation  for 
machine  design.  In  the  construction  of  any  machine,  however, 
theoretical  lines  can  seldom  be  followed  in  all  details,  and,  even  if 
this  were  possible,  the  truth  of  the  theory  must  be  demonstrated 
by  actual  trial  for  there  are  usually  many  factors  involved  which 
cannot  be  theoretically  considered  and  yet  affect  practical  results. 
In  any  machine  much  depends  upon  the  character  of  the  workman- 
ship, on  the  class  of  material  used,  and  on  all  the  details  of  manu- 
facture, installation  and  operation  as  well  as  on  design.  All  of 
these  matters  can  hardly  be  included  in  a  theoretical  consideration 
of  the  subject,  and  it  therefore  becomes  necessary  to  determine 
the  actual  results  attained  by  a  trial  of  the  machinery  under  work- 
ing conditions. 

General  observations  or  even  a  detailed  examination  of  any 
machine  and  its  operation  can  rarely  be  made  sufficiently  com- 
plete to  give  any  accurate  knowledge  of  the  quantity  or  quality  of 
the  results  which  it  can  and  does  accomplish.  It  is  only  when  the 
actual  effect  of  slight  changes  in  design  can  be  accurately  deter- 
mined by  careful  experiment  that  a  machine  can  be  improved  and 
practical  or  approximate  perfection  attained. 

The  ease  with  which  such  determination  can  be  made  is  usually 
a  criterion  of  the  rapidity  with  which  the  improvements  in  the  de- 
sign and  construction  of  a  particular  machine  take  place.  Where 
such  determinations  are  readily  made,  rapid  advancement  results, 
but  where  they  are  costly  and  require  a  considerable  expenditure 
of  time  or  money,  the  resulting  delays  and  expenses  usually  so 
limit  such  determinations  that  good  results  are  attained  but  slowly. 

The  invention  of  the  steam  engine  indicator  and  the  Piony  brake 
placed  in  the  hands  of  the  engineer  instruments  by  means  of  which 
he  could  readily  determine  the  action  of  steam  within  the  engine 
cylinder  and  the  actual  power  developed  therefrom.  The  knowl- 
edge thus  gained  has  been  one  of  the  most  potent  factors  in  the 
rapid  advancement  of  steam  engineering. 


35^  Turbine  Testing. 

The  physical  results  of  radical  modifications  or  changes  in  de- 
sign are  sometimes  quite  different  from  those  anticipated  by  the 
designer.  Improvement  in  any  machine  means  a  departure  from 
the  tried  field  of  experience  and  the  adoption  of  new  and  untried 
devices  or  arrangements.  Frequently  a  line  of  reasoning,  while 
apparently  rational,  is  found  to  be  in  error  on  account  of  unfore- 
seen conditions  or  contingencies  and  the  results  anticipated  are 
not  borne  out  in  the  actual  practical  results.  Unless,  therefore, 
such  results  are  carefully  and  accurately  determined  by  exact 
methods  the  actual  value  of  changes  in  design  may  never  be  known 
or  appreciated  and  designs  may  be  adopted  which,  while  apparently 
giving  a  more  desirable  form  of  construction,  actually  accomplish 
less  than  the  form  from  wrhich  the  design  has  departed. 

167.  The  Testing  of  Water  Wheels. — The  value  of  the  testing  of 
water  wheels  was  recognized  by  Smeaton  who-  tested  various 
models  of  water  wheels  about  the  middle  of  the  Eighteenth  Century. 
Methods  of  turbine  testing  were  also  devised  with  the  first  develop- 
ment of  the  turbine,  which  have  been  potent  factors  in  the  improve- 
ment of  the  turbine.  While  the  methods  of  testing  have  been 
greatly  improved  since  that  time,  they  have  not  as  yet  reached  a 
state  that  can  be  considered  reasonably  satisfactory,  and  turbine 
testing  has  not  become  so  general  as  to  assure  the  high  grade  of 
design  and  workmanship  in  their  manufacture  as  in  other  machin- 
ery where  testing  is  more  easily  and  regularly  practiced. 

The  principal  causes  of  the  backward  condition  of  turbine  test- 
ing lie  in  the  difficulties  and  expense  of  making  an  accurate  test 
in  place,  and  the  expense  and  unsatisfactory  results  of  testing  tur- 
bines in  a  testing  flume  where  the  head  and  capacity  are  so  limited 
as  to  confine  satisfactory  tests  to  heads  of  17  feet  or  less  and  to 
wheels  of  a  capacity  of  about  250  cubic  feet  per  second,  or  less  if 
the  full  head  of  17  feet  is  to  be  maintained.  There  is  an  urgent 
demand  for  accurate  and  economical  methods  for  the  measurement 
of  the  water  used  and  of  the  power  developed  by  water  wheels  in 
place,  that  can  be  readily  and  quickly  applied  without  the  almost 
prohibitive  expense  of  the  construction  of  expensive  weirs  and 
other  apparatus  now  used  for  such  purposes.  Apparently  slight 
variations  in  turbine  construction  produce  radical  changes  in  prac- 
tical results.  The  high  results  achieved  under  test  by  a  well- 
designed  and  well-constructed  wheel  is  no  assurance  that  wheels 
of  the  same  make  and  of  the  same  design,  even  though  they  be  ~>f 
the  same  size  and  even  from  the  same  pattern,  will  give  similar 


Smeaton's  Experiments. 


357 


results.  This  is  especially  true  when  the  contingencies  of  compe- 
tition and  the  knowledge  that  a  test  of  the  wheel  is  impossible,  or 
at  least  highly  improbable,  offer  a  premium  on  careless  construc- 
tion and  cheap  work. 

A  brief  examination  of  the  work  already  done  in  this  line,  and 
of  the  methods  now  in  vogue,  may  afford  suggestions  for  future 
improvements  and  development  in  this  important  wrork. 

1 68.  Smeaton's  Experiments. — John  Smeaton,  the  most  experi- 
enced and  eminent  engineer  of  his  time,  made  a  series  of  experi- 
ments on  the  power  and  effect  of  water  used  by  means  of  various 
forms  of  water  wheels  for  mill  purposes.  Accounts  of  these  experi- 
ments were  published  in  the  Transactions  of  The  Royal  Society  of 

England  in  1759.  Until  that 
time  the  relative  values  of  the 
different  types  of  water 
wheels  of  that  day  were  very 
poorly  understood  and  ap- 
preciated. 

Smeaton's  apparatus  for 
measurement  of  the  power 
of  overshot  and  undershot 
wheels  is  shown  by  Figs.  223 
and  224  taken  from  "The 
Encyclopedia  of  Civil  En- 
gineering" by  Edward 
Cressy.  Water  was  pumped 
by  means  of  the  hand  pumps 
from  the  tail  basin,  X,  to  the 
supply  cistern,  V,  from  which 
it  was  admitted  to  the  wheel 
through  an  adjustable  gate. 
The  power  developed  was 
measured  by  the  time  re- 


Fig.  223.— Smeaton's  Apparatus  for  Testing 
Water  Wheels. 


quired  to  raise  a  known 
weight  through  a  known 
height  by  means  of  a  cord 

passing  through  a  system  of  pulleys  and  attached  to  a  small  wind- 
ing drum  or  collar  upon  the  wheel  shaft.  This  drum  revolved  only 
when,  by  slight  longitudinal  movement,  it  was  made  to  engage  a 

pin  on  the  shaft. 

In  these  experiments   Smeaton  found  a  maximum  efficiency  of 


358 


Turbine  Testing. 


32  per  cent.,  and  a  minimum  efficiency  of  28  per  cent,  for  undershot 
wheels.  He  also  observed  that  the  most  efficient  relations  between 
the  peripheral  velocity  of  the  wheel  and  velocity  of  the  water  were 
attained  when  the  former  was  from  50  per  cent,  to  60  per  cent,  of 
the  latter,  and  that  the  force  that  could  be  exerted  by  a  wheel  to 


Fig  224.— Section  of  Smeaton's  Apparatus  for  Testing  Water  Wheels. 

advantage  was  from  50  per  cent,  to  70  per  cent,  of  tne  force  re- 
quired to  maintain  it  in  stationary  equilibrium. 

For  overshot  wheels  Smeaton  found  that  the  efficiency  varied 
between  52  and  76  per  cent.  From  his  experiments  he  concluded 
that  the  overshot  wheel  should  be  as  large  as  possible,  allowing, 
however,  a  sufficient  fall  to  admit  the  water  onto  the  wheel  with  a 
velocity  slightly  greater  than  that  of  the  circumference  of  the 
wheel  itself,  and  that  the  best  velocity  of  the  circumference  of  the 
wheel  was  about  three  and  one-half  feet  per  second.  This  speed 
he  found  applied  both  to  the  largest  as  well  as  to  the  smallest 
water  wheel. 

From  these  experiments  Smeaton  concluded  that  the  power  of 
water  applied  directly  through  the  exertion  of  its  weight  by  grav- 
ity, as  with  the  overshot  wheel,  was  more  effective  than  when  its 
power  was  applied  through  its  acquired  momentum,  as  in  the 


The  Early  Testing  of  Turbine  Water  Wheels.          359 

undershot  wheel,  although  his  line  of  reasoning  indicated  other- 
wise. The  later  development  of  impulse  wheels  shows  that  his 
reasoning  was  correct,  and  that  the  low  efficiency  of  the  impulse 
wheel  was  due  to  the  method  of  applying  the  momentum  of  the 
water  rather  than  to  any  inherent  defect  in  the  impulse  principle. 

The  experiments  or  tests  of  Smeaton,  while  crude  and  imperfect 
and  performed  upon  wheels  which  were  merely  models,  afforded 
a  comparative  measurement  of  the  efficiency  of  the  undershot,  over- 
shot and  breast  wheels  then  in  use  and  had  a  marked  effect  on  the 
further  selection  of  such  wheels. 

169.  The  Early  Testing  of  Turbine  Water  Wheels.— The  testing 
of  turbine  wheels  began  many  years  ago  in  France  before  the  turb- 
ine became  well  known  in  the  United  States.* 

Fourneyron  began  the  study  of  the  early  forms  of  turbines  as 
early  as  1823,  and,  in  1827,  he  introduced  his  well-known  wheel 
and  also  brought  into  notice  a  method  of  systematic  testing  of  the 
same  by  means  of  the  Prony  brake. 

"La  Societe  d'  Encouragement  pour  T  Industrie  Nationale"  is 
credited  by  Thurston  with  the  introduction  of  a  general  system  for 
the  comparison  of  wheels  and  correct  methods  of  determining  the 
efficiency.**  Other  engineers  immediately  accepted  this  method  of 
comparison  of  wheels.  Morin,  in  1838,  reported  the  results  of  a 
trial  of  a  Fourneyron  wheel  as  giving  an  efficiency  of  69  per  cent, 
with  only  slight  changes  in  values  for  a  wide  range  of  speed.  With 
another  wheel  he  obtained  75  per  cent,  efficiency.f 

Combes  tested  his  reaction  wheel  and  found  that  an  efficiency 
of  about  50  per  cent,  could  be  obtained.]! 

The  first  systematic  test  of  turbines  in  the  United  States  was 
made  by  Mr.  Elwood  Morris  of  Philadelphia  in  1843  and  reported 
in  the  Journal  of  The  Franklin  Institute  for  December  of  that  year. 

The  maximum  efficiency  reported  was  75  per  cent.  This  result 
was  reached  when  the  value  of  <£  for  the  interior  circumference  of 
the  Fourneyron  turbine  was  .45.  In  1844  Mr.  James  B.  Francis 
determined  the  power  and  efficiency  of  a  high  breast  water  wheel 


*  See  "The  Systematic  Testing  of  Water  Wheels  in  the  United  States,"  by 
ft.  H.  Thurston,  Trans.  Am.  Soc.  Mech.  Eng.  vol.  8. 

*::See  "Memoire  sur  les  Turbines  Hydrauliques,"    by  H.  Fourneyron,  Brus- 
sels, 1840. 

t  See  "Experiences  sur  les  Power    Hydrauliques,"   Paris,  1838. 

t  See  "Mechanics  of  Engineering,"  Weisbach.     Translated  by  A.  J.  DuBois. 
Hydraulics  and  Hydraulic  Motors,  vol.  II,  part  I,  p.  470. 


360 


Turbine  Testing. 


in  the  City  of  Lowell,  using  a  Prony  brake  fitted  with  a  dash-pot 
to  prevent  irregular  operation. 

In  1845  Mr-  Uriah  A.  Boyden  made  a  trial  of  a  turbine  designed 
by  himself,  using  the  Prony  brake,  and  obtained  an  efficiency  of  78 
per  cent,  as  the  maximum.  In  1846  a  similar  test  of  one  of  the 
Boyden  turbines  was  made  at  the  Appleton  Mills  in  Lowell,  and 
an  efficiency  of  88  per  cent,  was  reported.  He  continued  the  work 
of  the  testing  of  water  wheels  for  several  years  and  tested  many 
wheels  of  various  types.*  Mr.  Francis  introduced  the  system  of 
testing  wheels  which  were  to  be  used  by  purchasers  of  water  from 
the  water  power  company  which  he  represented.  The  chief  pur- 
pose of  the  tests  was  that  the  wheels  might  be  used  as  meters  in 
determining  the  amount  of  water  used  by  the  various  purchasers. 

In  1860  the  City  of  Philadelphia  undertook  a  comparative  trial 
of  various  turbines  in  order  to  determine  their  relative  merits  for 
used  in  the  Fairmount  Pumping  Plant.  The  results  o'f  these  tests 
given  in  Table  XXXIII  are  somewhat  questionable  but  have  a 
comparative  value. 

TABLE  XXXIII. 

Water  Wheel  Tests  at  Philadelphia  in  1860. 


Name  of  Wheel. 

Kind  of 
Wheel. 

Per 
cent 
of 
Effect 

3  per 
cent 
added 
for 
frict'n 

Where  built. 

Stevenson's  second  wheel  

Jonval    . 

.8777 

9077 

Paterson    N   J 

Geyelin's  second  wheel  

Jonval    . 

.8210 

8510 

Philadelphia    P^ 

Andrews  &  Kalbach's  third  wheel 
Collin's  second  wheel 

Spiral  .    . 
Jonval 

.8197 
7672 

.8497 
7972 

Bernville,  Pa. 
Trov   N   Y 

Andrews  &  Kalbach's  second 
wheel  

Spiral  .    . 

.7591 

.7891 

Bernville  Pa 

Smith's,  Parker's  fourth  trial  
Smith's,  Parker's  third  trial.  .... 
Steven's  first  wheel 

Spiral  .    . 
Spiral  .    . 
Jonval    . 

.7569 
.  7467 
7335 

.7869 
.7767 
7635 

Reading,  Pa. 
Reading,  Pa. 
Paterson  N   J 

Blake  

Scroll  .    . 

7169 

7469 

East  Pepperell    Mass 

Tyler  

Scroll  .    . 

.7123 

.7423 

West  Lebanon   N.  EL 

(jlevelin's  first,  wheel 

Jonval 

6799 

7099 

Philadelphia   Pa 

Smith's,  Parker's  second  wheel.  . 
Merchant's  Goodwin  

Spiral.    . 
Scroll  .    . 

.6726 
.6412 

.7026 
6712 

Reading,  Pa. 
G  nil  ford,  N   Y 

Mason's  Smith  

Scroll  .    . 

.  6324 

.6624 

Buffalo    N   Y 

Andrew's  first  whefl 

Spiral 

6205 

6505 

Bernville   PH 

Rich  

Scroll  . 

6132 

.6432 

Salmon  River   N  Y 

Littlepa^e  

Spiial.    . 

5415 

.5715 

Austin   Texas 

Monroe  

Scroll  .    . 

.5359 

.  5659 

Worcester   Mass 

Collin's  first  wheel         .    . 

Jonval 

4734 

5034 

Troy   N  Y 

*  See  "Lowell  Hydraulic  Experiments. 


The  Testing  of  Turbines  by  James  Emerson.  361 

170.  The  Testing  of  Turbines  by  James  Emerson. — One  of  the 

men  who  did  much  valuable  work  of  this  character  was  Mr.  James 
Emerson  who  designed  a  new  form  of  .dynamometer  of  the  trans- 
mitting kind.  At  the  request  of  Mr.  A.  M.  Swain,  Mr.  Emerson 
designed  a  Prony  brake,  embodying  this  dynamometer  for  the  pur- 
pose of  testing  a  Swain  turbine  in  a  flume  built  from  designs  by 
Francis.  The  results  obtained  by  Mr.  Emerson  from  this  test 
were  so  satisfactory  that  The  Swain  Turbine  Company  decided  to 
open  the  flume  for  the  purpose  of  a  competitive  test  of  all  turbines 
which  might  be  offered  for  this  purpose.  Announcement  of  this 
test  was  dated  June  i6th,  1869.  The  pit  was  fourteen  feet  wide, 
thirty  feet  long,  and  three  feet  deep,  measured  from  the  crest  of  the 
weir.  The  best  results  of  this  competitive  test,  the  accuracy  of 
which  has  since  been  .questioned  by  Mr.  Emerson,  were  attained 
with  the  Swain  and  Leffel  wheels.  The  former  ranged  from  66.8 
up  to  78.9  per  cent,  efficiency,  and  the  latter  from  61.9  to  79.9  per 
cent,  efficiency.  This  competitive  test  was  the  beginning  of  a  series 
of  such  tests  as  well  as  of  a  general  system  of  the  public  testing  of 
turbines.  The  testing  flume  was  opened  to  all  builders  and  users 
of  turbine  wheels  and  such  tests  have  been  continued  in  the  United 
States  up  to  the  present  time. 

The  report  of  the  results  of  this  test  attracted  the  attention  of 
Mr.  Stewart  Chase,  then  agent  of  The  Holyoke  Water  Power  Com- 
pany, who,  recognizing  its  very  great  importance,  secured  the 
adoption  of  a  systematic  testing  of  water  wheels  at  Holyoke  for 
the  benefit  of  the  Company  and  wrote  to  Mr.  Emerson  as  follows: 

'The  testing  of  turbines  is  the  only  way  to  perfection,  and  that 
is  a  matter  of  great  importance.  Move  your  work  to  Holyoke  and 
use  all  the  water  that  is  necessary  for  the  purpose,  and  welcome, 
free  of  charge." 

Mr.  Emerson,  who  had  been  conducting  the  testing  of  water 
wheels  as  a  matter  of  private  business  at  Lowell,  at  which  place 
he  was  obliged  to  pay  for  the  water  used,  at  once  accepted  the 
liberal  offer  thus  tendered  him  and  removed  to  Holyoke  where  he 
continued  the  testing  of  water  wheels  until  it  was  taken  in  hand 
by  The  Holyoke  Water  Power  Company. 

The  reports  of  Mr.  Emerson's  work  were  published  and  undoubt- 
edly were  the  means  of  bringing  a  number  of  wheels  up  to  a  state 
of  high  efficiency.  The  reports  were  found  to  be  full  of  valuable 


362 


Turbine   Testing. 


data,  and,  although  not  systematically  arranged,  formed  an  exten- 
sive and  valuable  collection  of  figures.* 

In  1879,  The  Holyoke  Water  Power  Company,  for  the  purpose  of 
determining  the  standing  of  wheels  offered  for  use  at  that  place, 


80 


70 


60 


so 


40 


30 
GATE 


|  GATE 


5  GATE 

Fig.  225. 


GATE 


FULL 
GATl: 


arranged  for  a  comparative  or  competitive  turbine  test  at  the  flume 
constructed  by  Mr.  Emerson  at  Holyoke.  The  wheels  were  set 
under  the  direction  of  Mr.  Emerson  and  a  part  of  the  tests  were 

*  See  James  Emerson's  "Hydro-Dynamics." 


The  Testing  of  Turbines  by  James  Emerson. 


made  or  witnessed  by  Mr.  Samuel  Weber  and  Mr.  T.  G.  Ellis. 
Their  report  was  accompanied  by  a  graphical  diagram  (Fig.  225 
and  Table  XXXIV)  on  which  they  commented  as  follows : 

"By  examining  the  diagram  and  table,  the  peculiarities  of  the 
several  wheels  will  be  readily  seen.  It  will  be  observed  that  the 
Houston  turbine,  which  has  the  highest  percentage  of  effect  at  full 
gate,  is  really  the  least  efficient  at  from  half  to  three-quarters,  and 
from  half  to  full  gate,  of  all  those  shown  on  the  diagram,  and  is 
only  superior  to  the  Nonesuch  at  from  three-quarters  to  full  gate, 
and  that  by  a  very  trifling  amount;  so  that  the  wheel  which  ap- 
parently has  the  highest  percentage  is  really  the  least  desirable  for 
actual  use.  The  Thompson  turbine,  which  has  the  lowest  percentage 
of  those  shown  at  full  gate,  rises  to  the  sixth  place  at  from  one-half 
to  full  gate,  and  to  the  fourth  place  at  from  one-half  to  three-quart- 
ers gate.  The  Tyler  turbine,  which  has  the  second  highest  per- 
centage at  full  gate,  falls  to  the  sixth  place  at  from  one-half  to 
three-quarters  gate.  The  Hercules  turbine,  which  stands  third 
only  at  full  gate,  takes  the  first  rank  at  from  half  to  full  gate,  or 
any  of  its  subdivisions.  The  New  American  turbine,  which  stands 
only  fifth  in  the  percentage  at  full  gate,  is  second  only  to  the  Her- 
cules at  from  one-half  to  full  gate  or  either  of  its  subdivisions,  and, 
indeed,  differs  from  the  Hercules  very  slightly  in  its  useful  effect 
through  the  whole  range  shown. 

"Taking  the  average  useful  effect  of  the  wheels  shown  from  one- 
half  to  full  gate  as  a  measure  of  their  efficiency,  their  relative  value 
is  in  the  order  shown  in  the  table." 


TABLE  XXXIV. 
Showing  Average  Percentage  at  Part  Gafe. 


Name. 

^toM 
Per  cent. 

%  to  Full 
Per  cent. 

K  to  Full 
Per  cent. 

.737 

.805 

.771 

.732 

.795 

.763 

.708 

.786 

.747 

Tyler  

.665 

.766 

.715 

Tait  

.680 

.744 

.712 

.696 

.721 

.709 

.619 

.712 

.666 

.397 

.717 

.557 

364 


Turbine  Testing. 


The  report  of  Mr.  Emerson  covered  a  much  larger  number  of 
wheels.  The  diagram  accompanying  Mr.  Emerson's  report*  is  re- 
produced in  Fig.  226. 


|  GATE 


FULL 
GATE 


Fig.  220. 

171.  The  Holyoke  Testing  Flume. — The  later  work  of  systematic 
testing  of  American  turbines  has  been  carried  on  principally  at  the 
Holyoke  flume. 

t  "The  object  aimed  at  by  the.  Water-power  Companies  of  Lowell 
and  Holyoke,  in  the  establishment  of  testing  flumes  for  turbines, 

*  Emerson's  "Hydro-Dynamics,"  page  300. 

f"The  Systematic  Testing  of  Water  Wheels,"  by  R.  H.  Thurston. 


The  Holyoke  Testing  Flume.  365 

is  the  determination  of  the  power  and  efficiency,  the  best  speed, 
and  the  quantity  of  water  flowing  at  from  whole,  to,  say,  half  gate, 
so  exactly  that  the  wheel  may  be  used  as  a  meter  in  the  measure- 
ment of  the  water  used  by  it.  The  quantity  of  water  passing 
through  the  wheel,  at  any  given  gate-opening,  will  always  be  prac- 
tically the  same  at  the  same  head,  and  the  wheel  having  been 
tested  in  the  pit  of  the  testing  flume,  and  its  best  speeds  and  highest 
efficiency  determined,  and  a  record  having  been  made  of  the  quan- 
tity of  water  discharged  by  it  at  these  best  speeds  and  at  all  gates, 
the  turbine  is  set  in  its  place  at  the  mill,  speeded  correctly  for  the 
head  there  afforded,  and  a  gauge  affixed  to  its  gate  to  indicate  the 
extent  of  gate  opening.  The  volume  of  water  passing  the  wheel 
at  various  openings  of  gate  having  been  determined  at  the  testing 
flume,  and  tabulated,  the  engineer  of  the  Water-power  Co.  has 
only  to  take  a  look  at  the  gauge  on  the  gate,  at  any  time,  or  at  regu- 
lar times,  and  to  compare  its  reading  with  the  table  of  discharges, 
to  ascertain  what  amount  of  water  the  wheel  is  taking  and  to  de- 
termine what  is  due  the  company  for  the  operation  of  that  wheel, 
at  that  time.  The  wheel  is  thus  made  the  best  possible  meter  for 
the  purposes  of  the  vender  of  water." 

The  present  Holyoke  Testing  Flume  was  completed  in  1883. 
The  plan  of  this  flume  is  shown  in  Figs.  227  and  228. 

The  testing  flume  consists  of  an  iron  penstock,  A,  about  nine  feet 
in  diameter,  through  which  the  water  flows  from  the  head  race 
into  a  chamber,  B,  from  which  it  is  admitted  through  two  head 
gates,  G,G,  into  the  chamber,  C,  and  from  thence  through  trash 
racks  into  the  wheel  pit,  D.  Passing  through  the  wheel  to  be 
tested,  it  flows  into  the  tail-race,  E,  where  it  is  measured  as  it 
flows  over  a  weir,  at  O.  The  object  of  the  chamber,  B,  is  to  afford 
opportunity  for  the  use  of  the  two  head  gates,  G,G,  to  control  the 
admission  of  water,  and  consequently  the  head  acting  on  the  wheel. 
There  is  also  a  head  gate  at  the  point  where  the  penstock,  A,  takes 
in  water  from  the  first  level  canal.  A  small  penstock,  F,  about  3 
feet  in  diameter,  takes  water  from  the  chamber,  B,  independently 
of  the  gates  and  leads  to  a  turbine  wheel,  H,  set  in  an  iron  casing, 
in  the  chamber,  C,  in  order  that  this  wheel  can  run  when  C  and  the 
wheel  pit,  D,  are  empty.  The  wheel,  H,  discharges  through  the 
floor  at  the  bottom  of  C,  and  through  the  arch,  I,  and  the  supple- 
mentary tail-race,  K,  into  the  second  level  canal.  This  wheel  is 
used  to  operate  the  repair  shops ;  also  to  operate  the  gates,  G.  The 
chamber,  C,  is  bounded  on  one  side  by  a  tier  of  stop-planks,  L,  and, 


366 


Turbine  Testing. 


The   Holyoke  Testing  Flume. 


367 


on  another  side,  by  a  tier  of  stop-planks,  M.  The  object  of  the 
stop-planks,  L,  is  to  afford  a  waste-way  out  of  the  chamber,  C. 
This  is  of  especial  use  in  regulating  the  height  of  the  water  when 
testing  under  low  heads.  The  water  thus  passed  over  the  planks, 
L,  falls  directly  into  the  tail-race,  K.  and  passes  into  the  second 
level.  The  stop-planks,  M,  are  used  when  scroll  or  cased  wheels 


Fig.  228.  -Testing  Flume  of  Holyoke  Water  Power  Co.  Arranged  for  Testing 
Horizontal  Turbines. 

are  tested.  In  such  cases  D  is  empty  of  water  and  the  wheefr  case 
in  question  is  attached  by  a  short  pipe  or  penstock  from  an  open- 
ing cut  in  the  planks,  M.  Flume  wheels  are  set  in  the  center  of  the 
floor  of  D,  and  D  is  filled  with  water.  They  discharge  through  the 
floor  of  D  and  out  of  the  three  culverts,  N,N,N,  into  the  tail-race, 
E.  Horizontal  wheels  are  set  in  the  pit,  D,  with  their  shafting 
projecting  through  a  stuffing-box  in  the  side  of  the  pit  (See  Fig. 
228).  At  the  down-stream  end  of  the  tail-race  is  the  measuring 
weir,  O  (Fig.  227).  The  crest  of  the  weir  is  formed  of  a  strip  of 
planed  iron  plate  twenty  feet  in  length.  The  depth  of  water  on  the 
weir  is  measured  in  a  cylinder,  P,  set  in  a  recess,  Q,  fashioned  in 
the  sides  of  the  tail-race.  These  recesses  are  water-tight,  and  the 
observer  is  thus  enabled  to  stand  with  the  water-level  at  convenient 


368  Turbine  Testing. 

height  for  accurate  observation.  The  cylinder,  P,  is  connected  with 
a  pipe  that  crosses  the  tail-race  or  weir  box  about  ten  feet  back  of 
the  weir  crest.  The  pipe  is  placed  about  one  foot  above  the  floor 
and  is  perforated  in  the  bottom  with  £  inch  holes.  A  platform,  R, 
surrounds  the  tail-race,  and  is  suspended  from  the  iron  beams  that 
carry  the  roof.  Above  the  tail-race  is  the  street,  over  which  the 
wheels  to  be  tested  arrive  on  wagons  from  which  they  are  lifted 
by  a  traveling  crane  that  runs  on  a  frame-work  over  the  street,  and 
by  means  of  which  the  wheels  are  carried  into  the  building  and  are 
lowered  into  the  wheel  pit,  D.  Spiral  stairs  lead  into  a  passageway 
that  leads  in  turn  to  the  platform,  R.  In  the  well-hole  of  these 
stairs  are  set  up  the  glass  tubes  which  measure  the  head  of  water 
upon  the  wheel.  These  gauge  tubes  are  connected  with  the  pit,  D, 
and  the  chamber,  C,  by  means  of  pipes,  one  of  which  enters  the 
wheel  pit  through  a  cast  iron  pipe,  T,  built  into  the  masonry  dam 
which  forms  the  down  stream  end  of  the  wheel  pit,  D.  The  other 
pipe  passes  back  under  the  wheel  pit,  D.  and  crosses  the  tail-race 
at  the  extreme  back  line  and  close  under  the  pit  floor.  This  pipe 
is  perforated  throughout  its  length  across  the  race  in  a  manner 
similar  to  the  pipe  used  for  determining  the  head  on  the  weir.  To 
enable  the  observers  at  the  brake  wheel,  head  gauge  and  measuring 
weir  to  take  simultaneous  olbservations,  an  electric  clock  rings 
three  bells,  simultaneously,  at  intervals  of  one  minute. 

The  usual  method  of  testing  a  wheel  is  as  follows :  After  the 
wheel  is  set  in  place  (See  Figs.  227  and  228)  a  brake  pulley  and 
Prony  brake  are  attached  to  the  shaft,  the  gates  are  set  at  a  fixed 
opening  and  water  is  admitted.  The  runaway  speed  of  the  wheel 
is  first  determined  with  the  brake  band  loose,  after  which  a  weight 
is  applied  and  the  brake  tightened  until  the  friction  load  balances 
the  weight.  As  soon  as  this  balance  is  attained,  which  requires 
only  a  few  seconds,  the  revolution  counter  is  read  and  the  heads 
in  the  head-race,  tail-race  and  on  the  weir  are  observed.  Observa- 
tions are  repeated  simultaneously  each  minute  at  the  stroke  of  the 
bell  and  for  a  period  of  from  three  to  five  minutes.  The  weight 
is  then  changed  and  the  observations  repeated  for  a  different  load 
and  speed.  After  observations  are  made  over  the  range  of  speeds 
desired,  the  gate  opening  is  changed,  and  a  similar  series  of  obser- 
vations are  made  for  the  new  gate  opening.  This  is  repeated  for 
each  desired  gate  opening,  usually  from  full  gate  to  about  one-half 
gate. 

The  results  are  calculated  and  reported  in  the  form  shown  in 
Table  LX.  It  is  usually  stated  in  the  report  whether  the  test  is 


The  Value  of  Tests.  369 

made  with  a  plain  or  conical  draft  tube,  whether  plain  or  ball  bear- 
ings are  used,  and  also  the  pull  necessary,  at  a  given  leverage,  to 
start  the  turbines  in  the  empty  pit.  No  attempt  is  made  in  these 
reports  to  describe  the  bearings  or  finish  of  the  wheels  in  detail. 

The  maximum  head  available  is  about  17  feet  under  small  dis- 
charges and  this  decreases  to  about  9  feet  under  a  discharge  of  300 
cubic  feet  per  second.  The  capacity  of  the  tail-race  and  weir  is 
hardly  sufficient  for  the  accurate  measurement  of  the  latter  quan- 
tity. 

172.  The  Value  of  Tests. — There  can  be  no  question  as  to  the 
very  great  value  of  carefully-made  tests  of  any  machine.  It  must 
be  borne  in  mind,  however,  that  any  test  so  made  represents  results 
under  the  exact  conditions  of  the  test,  and,  in  order  to  duplicate  the 
results,  the  conditions  under  which  the  test  'was  made  must  be 
duplicated.  Any  changes  in  the  design  or  finish  of  the  wheels,  any 
alterations  in  the  method  of  setting,  or  in  the  gates,  draft  tube  or 
other  appurtenances  connected  with  the  same  are  bound  to  affect 
the  power  and  efficiency  to  a  greater  or  less  extent. 

It  is  unfortunate  for  the  world's  progress  that  the  records  and 
conditions  of  failures  are  seldom  made  known.  The  record  of  a 
failure,  while  of  great  value  from  an  educational  standpoint,  may 
considerably  injure  the  reputation  of  an  engineer  or  manufacturer, 
and  consequently  results  of  tests  and  experiments,  unless  fully 
satisfactory,  are  seldom  published  or  known  except  by  those  closely 
interested.  For  this  reason,  the  published  tests  of  water  wheels 
usually  represent  the  most  successful  work  of  the  maker  and  the 
best  practical  results  he  has  been  able  to  secure.  Tests,  unless 
fairly  representative,  do  not  assure  that  similar  turbines  of  the 
same  make,  or  even  similar  turbines  of  the  same  make,  size  and 
pattern,  will  give  the  same  efficient  results  unless  all  details  of  their 
design,  construction,  and  installation  are  duplicated.  There  is  no 
doubt  that  in  many  cases  the  published  tests  of  water  wheels  are 
the  final  consummation  of  a  long  series  of  experiments,  made  in 
order  to  secure  high  results,  and  do  not  give  assurance  that  such 
results  can  be  easily  duplicated.  The  manufacturers  have  acknow- 
ledged this  by  calculating  their  standard  tables  on  a  basis  of  power 
and  efficiency  below  that  of  the  best  tests  they  are  able  to  obtain, 
and  it  is  only  a  matter  of  reasonable  precaution  for  the  engineer, 
who  is  utilizing  the  results  of  any  such  tests  for  the  purposes  of 
his  design,  to  discount  the  test  values  to  such  an  extent  as  will 
assure  him  that  his  estimates  will  be  fulfilled. 


370  Turbine  Testing. 

In  water  wheels  for  high-grade  work,  it  is  important  that  the 
specifications  for  their,  construction  be  carefully  drawn  and  that, 
by  inspection  and  tests,  the  results  of  the  work  be  fully  assured. 
It  is  unfortunate  that  no  easily  applied  method  is  available  for  the 
testing  of  water  wheels  in  place.  Such  tests  as  are  now  carried  on 
involve  the  shipment  of  one  or  more  of  the  wheels  from  the  place 
of  manufacture  to  Holyoke,  their  tests  under  the  conditions  there 
obtainable  and  their  reshipment  to  the  point  where  they  are  to  be 
installed.  Here  they  may  be  set  to  operate  under  conditions  en- 
tirely different  from  those  of  the  Holyoke  test  and  the  actual 
results  obtained  cannot  usually  be  determined.  The  most  satisfac- 
tory test  of  any  machine  is  a  test  made  under  the  conditions  of 
actual  service,  and,  when  such  tests  can  be  made,  the  results  are 
much  more  definite  and  of  greater  value  than  the  tests  of  the  wheel 
made  under  conditions  entirely  different  from  those  under  which  it 
is  to  operate. 

The  Holyoke  Testing  Flume  is  performing  valuable  service  and 
the  results  of  its  work  have  been  of  material  assistance  in  the  de- 
velopment and  improvement  of  a  number  of  high  grade  wheels. 
Much  remains  to  be  done,  however,  in  the  development  of  turbine 
testing  so  as  to  make  it  possible  to  more  readily  determine  results 
under  working  conditions.  More  uniform  work  will  undoubtedly 
result  as  the  mechanical  methods  of  manufacture  improve  and  man- 
ufacturers are  able  to  more  nearly  duplicate  the  satisfactory  con- 
ditions which  they  have  found  to  obtain  in  special  cases. 

173.  Purpose  of  Turbine  Testing. — Water  turbines  may  be  tested 
for  various  purposes  among  which  may  be  named: 

1.  To  establish  the  general  principles  of  the  operation  of  such 
wheels. 

2.  To  ascertain  the  most  favorable  condition  for  the  operation 
of  a  particular  type  of  wheel. 

3.  To  ascertain  the  results  of  operating  a  particular  wheel,  or 
size  or  type  of  wheel,  under  particular  conditions. 

4.  To  investigate  the  various  losses  in  the  turbine  in  order  that 
such  losses  may  be  reduced  as  low  as  possible. 

The  quantities  to  be  measured  in  a  water  wheel  test  are  revolu- 
tions per  minute  or  speed,  discharge,  and  power  output. 

In  the  fourth  case  the  determination  of  heads,  velocities  and 
friction  losses  at  various  points  in  the  wheel  case  and  wheel  may 
be  essential. 

The  extent  to  which  a  test  should  be  carried  will  depend  on  its 


Factors  that  Influence  the  Results  of  a  Test.  371 

purpose.  For  the  first  purpose  above  mentioned  the  range  of  ex- 
periments should  be  as  complete  as  possible,  the  discharge,  and 
power  of  the  wheel  being  determined  from  numerous  speeds  from 
zero  to  the  runaway  value  and  at  various  heads  within  the  limits 
of  the  physical  conditions. 

For  the  second  purpose  mentioned,  the  test  may  be  carried  only 
through  the  range  of  commercial  conditions  under  which  the  wheel 
would  ordinarily  operate,  but  should,  however,  be  broad  enough  to 
include  the  range  of  conditions  which  will  obtain  in  practice  due 
to  the  variations  in  head  which  are  anticipated  at  various  seasons. 

For  the  third  purpose  mentioned,  the  wheel  need  be  tested  only 
under  the  particular  condition  for  which  information  is  desired. 
The  test  may  be  to  determine  whether  or  not  certain  guarantees 
of  the  manufacturer  have  been,  or  will  be,  fulfilled. 

For  the  fourth  purpose  a  special  line  of  investigation  and  tests 
are  necessary,  which,  while  of  great  importance,  are  of  special  in- 
terest to  the  manufacturer  only  or  to  those  interested  in  the  detail 
development  of  some  wheel  for 'special  purposes. 

For  the  purpose  of  any  test  a  clear  conception  of  the  nature  of 
the  information  sought  is  essential  and  each  determination  must 
be  made  with  proper  precaution  in  order  to  secure  accurate  results, 
174.  Factors  that  Influence  the  Results  of  a  Test. — It  is  appar- 
ent from  the  principles  discussed  in  Chapter  II  that  the  actual 
power  developed  by  a  turbine  will  be  somewhat  less  than  the 
theoretical  power  of  the  water  passing  into  it,  depending  on  the 
character  of  the  wheel  and  the  various  energy  losses  involved  in  its 
operation.  The  efficiency  of  the  wheel,  representing  the  ratio  of 
power  developed  to  power  applied,  depends  on  the  same  factors. 

These  losses,  incidental  to  the  operation  of  a  turbine,  include  the 
friction  of  the  shaft  on  its  bearings,  the  hydraulic  resistance  from 
the  friction  and  shock  of  the  water  in  the  guides  and  passages,  the 
slip  or  leakage  between  the  fixed  and  revolving  parts  of  the  wheel, 
and  the  unutilized  energy  due  to  the  velocity  remaining  in  the 
water  when  discharged  from  the  wheel. 
These  losses  are  estimated  as  follows  :* 

Shaft  friction from    2  to    3  per  cent. 

Slip  or  leakage from    2  to    3  per  cent. 

Hydraulic  friction  and  f^hock from  10  to  15  per  cent. 

Energy  in  water  leaving  wheel from    3  to    7  par  cent. 

Total  loss  of  energy from  17  to  28  per  cent 


*  See   "Development  of  Transmission    of    Power,"  by    Unwin,  p.    104;   also- 
•'Francis  Turbinen,"  by  Muller,  p.  18. 


37 2  Turbine  Testing. 

The  total  lasses  given  above  correspond  well  with  current  prac- 
tice. Under  the  best  conditions  efficiencies  greater  than  83  per 
cent,  are  often  obtained,  and,  under  unfavorable  conditions  with 
poor  design  and  poor  construction,  efficiencies  much  less  than  the 
minimum  of  72  per  cent,  are  common.  While  these  losses  can  never 
be  entirely  obviated  they  should  be  reduced  to  the  practical  mini- 
mum that  good  design  and  good  workmanship  will  permit. 

175.  Measurement  of  Discharge. — The  discharge,  q,  of  the  wheel 
is  commonly  measured  in  cubic  feet  per  second  and  should  repre- 
sent only  the  actual  discharge  through  the  wheel  itself.  This  dis- 
charge is  usually  measured,  after  it  has  passed  the  wheel,  by  the 
flow  over  a  standard  weir.  Any  leakage  around  the  wheel  into  the 
weir  box  or  from  the  weir  box  around  the  weir  must  be  determined 
and  deducted  from  or  added  to  the  amount  passing  the  weir.  The 
actual  weir  discharge  must  be  known  either  by  a  direct  calibration 
of  the  weir  or  by  the  construction  of  the  weir  on  lines  for  which 
the  discharge  coefficients  are  well  established.  Errors  in  weir 
measurements  often  reach  values  of  nearly  5  per  cent,  due  to  the 
erroneous  use  of  coefficients  obtained  from  other  weirs  not  strictly 
comparative. 

The  head  on  the  weir  must  be  accurately  determined  by  means 
of  a  hook  gauge  which  should  usually  read  to  .001  of  a  foot.  An 
error  of  .01  foot  in  reading  the  head  on  the  weir  represents  about  i 
per  cent.,  and  an  error  of  .001  about  .1  per  cent.,  in  the  computed 
discharge  with  a  1.5  foot  head  on  the  weir  and  a  much  greater  error 
at  a  lower  head. 

The  construction  of  weirs  in  the  tail-race  of  power  plants,  es- 
pecially where  large  quantities  of  water  are  used  under  low  heads, 
involves  an  expense  which  is  often  prohibitive.  In  addition  to  this, 
the  construction  of  such  weirs  in  plants  working  under  low  heads 
wooild  often  seriously  reduce  the  head  and  alter  the  working 
•conditions. 

Other  methods  of  accurately  determining  the  flow  should  be 
•developed.  There  are  two  methods  which  seem  to  give  promise 
of  good  results: 

First:  By  the  careful  determination  of  the  velocities  of  flow  in 
the  cross-section  of  the  head  or  tail-race  at  points  far  enough  from 
the  wheel  to  guarantee  steady  flow.  This  may  be  done  by  means 
of  a  carefully  calibrated  current  meter,  a  pitot  tube,  or  by  floats 
To  secure  good  results  these  instruments  must  be  in  the  hands  of 


Measurement  of  Head.  373 

one  familiar  with  their  use  and  with  the  sources  of  error  to  which 
each  is  liable  if  carelessly  used.  (See  Chapter  XL)  This  method  in- 
volves no  loss  in  head. 

Second :  By  the  construction  in  the  head  or  tail  race  of  sub- 
merged orifices  of  known  dimensions  and  of  a  character  for  which 
the  coefficient  of  discharge  has  been  determined.  Some  work  in 
this  line  has  been  done  at  the  University  of  Wisconsin  (See  pages 
43  to  45)  which  will  soon  be  made  accessible  in  detail  in  a  bulletin 
now  in  press.  This  method  will  involve  only  small  losses  of  head 
and  by  a  sufficient  range  of  experiments  can  perhaps  be  made 
nearly  as  accurate  as  weir  measurements. 


Fig.  229.— Doble  Tangential  Wheel  Arranged  for  Brake  Test. 

176.  Measurement  of  Head. — The  power  of  water  applied  to  the 
wheel  depends  on  both  quantity  and  head.    The  head  is  more  easily 
measured  than  the  quantity,  but,  nevertheless,  requires  consider- 
able care  for  its  accurate  determination. 

The  head  of  the  wheel  must  be  measured  immediately  at  the 
wheel  both  for  the  head-water  and  tail-water.  If  measured  some 
distance  away  it  is  apt  to  include  friction  losses,  which  should  not 
be  charged  against  the  wheel  in  raceways,  penstocks  and  gates. 
The  measurement  of  head  should  usually  be  to  about  .01  feet,  al- 
though this  depends  on  the  magnitude  of  the  heads  involved. 

177.  Measurement    of    Speed    of    Rotation. — The    speed    of    the 
wheel  is  usually  recorded  in  revolutions  per  minute  and  may  be 


Turbine  Testing. 


230.— Section  and  Plan  of  Apparatus  for  Testing  Swain  Turbine  (by 
James  B.  Francis). 


Measurement  of  Power.  375 

determined  by  a  revolution-counter  which  records  the  number  of 
revolutions  made  in  a  given  interval  of  time ;  or  by  a  "tachometer" 
which,  by  means  of  certain  mechanism,  indicates  at  once  on  a  dial 
the  revolutions  per  minute.  The  latter  method  is  more  convenient 
if  the  instrument  is  correct,  but  frequent  calibration  and  adjustment 
are  necessary  and  a  correction  must  usually  be  applied  to  values 
thus  observed. 

The  revolution-counter  is  more  accurate,  and,  while  not  so  con- 
venient, is  to  be  preferred. 

178.  Measurement  of  Power. — The  power  of  the  wheel  may  be 
determined  by  placing  a  special  brake  pulley  on  the  turbine  shaft 
and  applying  a  resistance  by  means  of  a  Prony  brake  or  some  other 
form  of  dynamometer.     This  resistance  is  then  measured  by  some 
form  of  scales  (See  Figs.  229  and  230).    The  power  thus  consumed 
by  the  friction  of  the  brake  can  be  calculated  by  equation  (i) 

2/r  1  n  w 

W     Pl       33000    ^  which 
P  =  Horse  power 

1  =  length  of  lever  or  brake  arm  from  center  of  revolution,  in  ft. 
n  =  revolution  per  minute. 

it  =  ratio  of  the  circumference  to  the  diameter  of  a  circle  =  3.1416. 
w  =  weight  on  the  scale  in  pounds. 

This  is  the  method  applied  in  all  laboratory  work  (see  Fig.  229)  and 
is  that  used  at  the  Holyoke  Testing  Flume.  If  properly  applied, 
it  is  probably  subject  to  minimum  error.  When  wheels  are  tested 
in  place,  it  is  sometimes  more  convenient,  and  often  essential,  to 
determine  the  power  output  from  the  current  generated  by  elec- 
trical units,  which,  when  measured  by  aid  of  the  known  efficiency 
of  the  generator,  will  give  the  actual  power  of  the  wheel.  If  these 
units  be  direct-connected  so  that  little  or  no  transmission  loss  is 
involved,  and  if  the  generator  is  new  and  its  efficiencies  have  been 
accurately  determined,  the  errors  involved  by  this  method  are 
comparatively  small.  The  transmission  of  the  power  before  mea- 
surement through  gearing,  through  long  shafts  and  bearings  or  by 
other  means,  involves  losses,  the  uncertainties  of  which  must  be 
avoided  if  accuracy  is  essential. 

179.  Efficiency. — The   efficiency   of   a    machine    is    the    ratio    of 
energy  delivered  by  the  machine  to  that  which  was  supplied  to  it 
and  it  may  have  various  significations. 

In  an  impulse  wheel  (See  Section  152)  the  theoretical  energy  of 
the  water  in  the  forebay  in  foot  pounds  per  second  is : 
(2}  E  --  qwh 


376 


Turbine  Testing. 


The  energy  just  inside  the  outlet  of  the  pipe  is 

(3).  Ex  =qw(h'  +  h") 

The  energy  of  the  jet  is 

(4)  E*  =  ^ir          ' 

and  the  theoretical  power  delivered  to  the  bucket  is 

qw  (1  —  <?)  v  (1  —  cos  a)  cp  v 

E.=  -5- 

If  e  represents  the  actual  ft.  Ibs.  of  work  delivered  by  the  wheel 
per  sec.  then 

(6)  — g—  =  the  efficiency  of  the  entire  installation  including  pipe,  jet, 

wheel,  etc. 

(7)  -fir-  =  efficiency  of  the  water  wheel,  including  nozzle  and  buckets, 


(8) 


=  efficiency  of  the  runner,  and 


(9)     -jg—  =  hydraulic  efficiency  of  the  bucket 

In  the  testing  of  water  wheels,  the  efficiency  (7),  -g-,   is   the  ratio- 
ordinarily  to  be  determined  since  it  involves  the  losses  in  the  noz- 

1  u_ 


II 


"Bolt 


1 

1 

1 

1 

1 

1 

I 

1 

1 

1 

1 

1 

"\                      1" 

1 

1 

1 

1 

I 

1 

Half  End  Elevation 
W.O.Weber 


Half  Sectional 
Side  Elevation 


Fig.  231. 

zle,  jet  and  buckets  as  well  as  from  residual  energy  in  the  water 
discharged  by  the  buckets,  all  of  which  are  properly  chargeable  to 
the  operation  of  the  wheel. 


Measurement  ot  Power. 


377 


End  Elevation  of  Rings 

W.o.  freber  Part  Side  Elevation 


End  Elevation 

...  W.O.  Wetter 


Fig.  232. 


Flan 


Fig.  233. 


The  efficiency  represented  by  (9)  involves  only  the  effects  of 
losses  of  energy  by  the  water  in  passing  over  the  buckets  and 
its  theoretical  value  is  100  per  cent,  for  all  values  of  0.  It  elim- 
inates the  effect  of  uneconomical  speed  of  rotation  of  the  wheel 
which  leaves  residual  lost  energy  in  the  water  discharged  by  the 
buckets  and  not  properly  chargeable  to  bucket  imperfections.  It 
23 


378 


Turbine  Testing. 


would  be  determined  only  in  a  detailed  study  or  test  made  for  the 
first  purpose  above  mentioned. 

1 80  Illustration  of  Methods  and  Apparatus  for  Testing  Water 
Wheels: — Fig.  230  shows  the  apparatus  used  for  testing  turbines 
on  a  vertical  shaft,  by  Mr.  J.  B.  Francis  to  test  a  Swain  wheel  at  the 


aoo 


BO  70 

PER  CENT  BATE  OPENING 


80 


Fig.  234. 

Boott  Mills,  Lowell,  Massachusetts  (See  "Lowell  Hydraulic  Ex- 
periments.") 

The  section  represents  a  vertical  turbine  in  the  testing  plant  with 
testing  apparatus  in  place. 

The  plan  of  the  plant  shows  the  arrangement  of  the  Prony  brake. 

In  these  drawings  P  is  the  friction  pulley ;  b  is  the  brake ;  c  are 
counter  balances  to  remove  the  load  of  the  brake  from  the  wheel 
shaft;  L  is  the  bent  lever  or  steel  beam  for  transferring  horizontal 
motion  to  a  vertical  lift;  S  is  the  scale  pan  for  the  weight;  d  is  the 
dash-pot;  w  is  the  weir  for  measuring  the  water,  and  r  is  the  rack 
for  stilling  the  water  after  leaving  the  wheel. 

Figs.  231,  232,  233,  show  the  brake  wheel  and  Prony  brake  de- 
tails used  by  Mr.  William  O.  Weber  for  determining  the  efficiency 


Tests  of  Wheels  in  Place. 


379 


of  various  turbine  water  wheels  as  described  by  him  in  a  paper  on 
"The  Efficiency  Tests  of  Turbine  Water  Wheels,"  (See  vol.  27,  Xo. 
4,  American  Society  of  Mechanical  Engineers).  (See  also  Section 
171,  Experiments  at  the  Holyoke  Testing  Flume.) 

181.  Tests  of  Wheels  in  Place. — In  April,  1903,  a  Leffel  turbine 
was  tested  at  Logan,  Utah,  at  the  station  of  The  Telluride  Power 
Transmission  Company,  by  P.  N.  Nunn,  Chief  Engineer.  The 
wheel  was  directly  connected  to  a  General  Electric  generator  the 
efficiency  of  which  has  been  determined  as  follows : 

125  per  cent  load 96.7  per  cent,  efficiency     . 

100  per  cent  load 96 . 2  per  cent,  efficiency 

75  per  cent  load 95.3  per  cent,  efficiency 

50  per  cent  load 93 . 5  per  cent,  efficiency 

25  per  cent  load 88 . 0  per  cent,  efficiency 

The  output  of  this  generator  was  used  as  a  basis  for  calculating 
the  work  done  by  the  water  wheel. 

The  results  of  the  tests  and  methods  of  calculation  are  shown  in 
Table  XXXV  and  graphically  illustrated  in  Fig.  234. 

TABLE  XXXV. 

Test  of  High  Head  Leffel  Horizontal  Turbine  at  Logan  Station  of  Telluride 
Power  Trans.  Company,  Logan,  Utah.  Efficiency  of  Test  at  Constant  Speed, 
April  28,  1908. 

P.  N.  Nunn,  Chief  Engineer. 


Gate  opening  

0  75 

0.50 

0.40 

0  50 

0  75 

0  % 

HeaM  on  15  feet  weir  in  feet 
Discharge  of  weir  in  cubic  feet 
per  second 

1.394 
81  85 

1.132 
59  76 

0.969 

47  27 

1.129 
59  66 

1.368 
79  55 

1.475 
88  °)4 

Leakage  around  weir  in  sec- 
ond, feet 

0  85 

0  85 

0.85 

0.85 

0  85 

0  85 

Exciter  water  in  second  feet 
Water  through    turbine    in 
second  feet  

1.98 
80.72 

1.98 
58.63 

1.98 
46.14 

1.98 
58.53 

1.98 
78.42 

1.98 
87  81 

Pressure  at  shaft  center  in 
pounds  per  square  inch  .  . 
Effective  head  above  shaft 
center  in  feet 

86.5 
199.3 

87.3 
201.2 

87.5 
201.6 

87.2 
200.9 

86.5 
199.3 

86.2 
IPS  6 

Vacuum  head    measured  in 
feet  

10.4 

10.6 

10.8 

10.6 

10.4 

10.3 

Total  working  head  in  feet 
Theoretical  horse  power  .... 
K.W.  output  at  Sw.  Bd  
Generator  efficiencv  

209.7 
1921 
1152 
0.965 

211.8 
1409 
739 
0.952 

212.4 
1112 
500 
0.935 

211.5 
1405 
737 
0.952 

209.7 
1866 
1123 
0.965 

208.9 
2082 
1210 
0.967 

Brake  horse  power  of  turbine 
Efficiencv  of  turbine  

1600 
0.833 

1041 
0.738 

717 
0.644 

1038 
0.739 

1560 
0.836 

1677 
0.806 

Gate  opening  

0.75 

0.50 

0.40 

0.50 

0.75 

0.96 

NOTE— Speed,  400  K.  P.  M.  (normal). 

Generator  efficiency  taken  from  test  of  machine  made  by  The  General  Electric 
Company.     (Record  of  test  in  office  of  chief  engineer). 


380 


Turbine  Testing. 


A  similar  test  of  one  of  a  number  of  wheels  installed  by  The 
James  Leffel  Company  in  the  plant  of  the  Niagara  Hydraulic 
Power  and  Manufacturing  Company  was  made  in  December,  1903, 
by  Mr.  John  L.  Harper,  engineer  of  that  company.  The  following 
table  XXXVI  is  the  condensed  data  of  the  test  of  wheel  No.  8 
which  is  also  illustrated  by  Fig.  235. 


89 

^ 

^rf- 

1  7O 

/ 

^ 

/ 

•^   ~~~ 

^^ 

^ 

1  BO 

/ 

x 

/ 

^--  —  ' 

-—  — 

-       '< 

1  50  Q 

*/ 

/ 

/ 

' 

/ 

^ 

Z 

o 

140  m 

,< 

f 

/ 

/ 

/ 

m 
1  30  £» 

t 

, 

/ 

/ 

n. 

| 

IENCY 
R  0 

R  C 

/ 

i 

¥ 

/ 

ui 

k. 

1  1  0 

o  •• 

U. 

E 

f 

.  f 

7 

tn 

o> 

Z 
1800 

4-S 

/ 

i 

£/ 

.   -r^. 

Z 

BO 

2 

7 

/A 

UI 

u 
or 

/ 

i 

*    2 

/ 

IDDD 

25 

\J 

5Q 

f 

BO 


55    BO    85    70   75    80 
PER  CENT  GATE  OPENING 


85   80   95 


Fig.  235. 

The  water  was  measured  by  a  standard  contracted  weir  16.23 
feet  long  and  discharge  computed  by  Francis'  formula: 

q  =  3.33(L—  0.2h)  h§ 

The  load  was  computed  from  the  voltmeter  and  ammeter  read- 
ings of  two  generators  Nos.  5  and  12  which  were  both  driven  by 
this  wheel  and  then  corrected  for  the  generator  loss  by  a  factor 
estimated  from  the  shop  tests  of  the  generators. 


Tests  of  Wheels  in  Place. 


TABLE  XXXVI. 

Test  of  a  Double  Horizontal  Leffel  Turbine  installed  in  the  plant  of  the 
Niagara  Hydraulic  Company,  Niagara  Falls,  N.  Y. 


GATE  OPENING. 

.45 

.7 

1.0 

Dec.  5th 

Dec.  6th 

Xiine                            

3:21  p.  m. 
1.365 
84.76 
213.0 
2045 
255 

178 
5065 
.92 
1314 

Friction 
Load 
Only 
17 
1331 
.651 

5:01  p.  m. 
1.978 
146.6 
212.4 
3528 
259 

178 
5020 
.92 
1302 

12200 
57.7 
.95 
1720 
3022 
.856 

4:59  p.  m. 
2.257 
178.3 
212.7 
4320 
250 

184 
5833 
.92 
1563 

13000 
60.5 
.955 
1912 
3475 
.805' 

Hook  gaujje  readin0*  (corrected)            . 

Discharge  of  wheel  by  Francis'  formula 

Head  on  turbine  

Hydraulic  horse  power 

R.  P.  M  

Generator  No.  5* 
V0]ts  

Amperes    

Efficiency  

Horse  power  taken  from  wheel  by  generator  .... 

Generator  No.  12** 
Volts                       

Efficiency  

Horse  power  taken  from  wheel  by  generator  
Total  horse  power  output  of  wheel  

Efficiency  of  wheel  

8000 


4000  6000  8000 

HORSE    POWER 

Fig.  236. 


10000 


9GO 


800  a 


700 


600 


500  £ 


400  5 


3002 


200 


100  a 


12000 


*  Generator  No.  5  is  a  G.  E.  5000  A.  175  V.,  D.  C.  machine. 

**  Generator  No.  12  is  a  Bullock  1000  W.  W.,  3  phase  A.  C.  generator. 


332 


Turbine  Testing. 


The  10,500  h.p.  turbine  manufactured  by  the.  I.  P.  Morris  Com- 
pany for  the  Shawinigan  Power  Company  was  also  tested  in  a 
similar  mariner.  A  brief  outline  of  this  test  is  given  on  page  416 
The  graphical  result  of  the  same  is  shown  by  Fig.  236.  Fig.  237 
illustrates  the  test  of  a  25"  Victor  High  Pressure  Turbine,  manu- 
factured by  the  Platt  Iron  Works  Co.,  at  the  Houck  Falls  Power 
Station  at  Ellensville,  New  York. 

The  results  of  various  tests  at  the  Holyoke  Testing  Flume,  col- 
lected from  divers  sources,  are  given  in  the  appendix.  Most  of  the 
later  tests  have  been  furnished  by  manufacturers  and  represent  the 
best  results  of  modern  turbine  manufacture. 


70 


8° 


tf> 


609 


SCO 


300 


"1.0 


200   .8 


.i<: 

a 


200         400         600         800         1000       1200        1400       1600       4800       2000      2200      8400 
DISCHARGE  IN   CUBIC    FEET    PER     MINUTE/ 


.2 


0   0 


Fig.  237. 


Literature.  383 


LITERATURE. 

TURBINE  TESTING. 

1.  Smeaton,  James.     "An  Experimental  Inquiry,  read  in  the  Philosophical 

Society  of  London,  May  3rd  and  10th,  1759,  concerning  the 
Natural  Powers  of  Water  to  Turn  Mills  and  Other  Machines, 
Depending  on  a  Circular  Motion." 

2.  Morin.     "Experiences  sur  les  Power  Hydraulicques."     Paris,  1838. 

3.  Fourneyron,   H.     "Memoire  sur  les  Turbines  Hydraulicques."     Brussels, 

1840. 

4.  Francis,  J.  B.     Tests  of  Several  Turbines  Including  the  Tremont-Fourney- 

ron  and  the  Boott  Center  Vent  Wheels.  Lowell  Hydraulic  Ex- 
periments, 1847-1851. 

5.  Francis,  J.  B.     Test  of  Humphrey  Turbine,  275  h.  p.     Trans.  Am.  Soc. 

C.  E.,  vol.  13,  pp.  295-303.     1884. 

6.  Webber,  Samuel.     Turbine  Testing.     Elec.  Rev.  Oct.  18,  1895,  p.  477. 

7.  Webber,  Samuel.     Instructions  for  Testing  Turbines.     Eng.  News,  1895. 

Vol.  2,  p.  372. 

8.  Cazin,  F.  M.  F.     The  Efficiency  of  Water  Wheels.     Elec.  Wld.  Jan.  9,  1897. 

9.  Report  of  Tests  of  a  28-inch  and.  36-inch  "Cascade"  Water.  Wheel.     Jour. 

Fr.  Inst.     May,  1897. 

10.  Hitchcock,  E.  A.     Impulse  Water  Wheel  Experiments.    Elec.  Wld.     June 

5,  1897. 

11.  Hatt,    W.    Kendrick.     An    Efficiency    Surface    for    Pelton    Motor.     Jour. 

Franklin  Inst,  June,  1897,  vol.  143,  p.  455. 

12.  Thurston,  R.   H.     Systematic  Testing  of  Turbine  Watev  Wheels  in  the 

United.  States.     Am.  Soc.  Mech.  Eng.  1897,  p.  359. 

13.  Results  of  Tests  of  Cascade  Wheel.     Eng.  News,  1897,  vol.  2,  p.  27 

14.  Results  of  Tests  of  Hug  Wheel.     Eng.  News,  1898,  vol.  2,  p.  327. 

15.  Efficiency  Curves.     Eng.  News,  1903,  vol.  2,  p.  312. 

16.  Houston,  W.  C.     Tests  with  a  Pelton  Wheel.    Mech.  Engr.,  May  30,  1903. 

17.  Henry,  Geo.  J.,  Jr.    Tangential  Water  Wheel  Efficiencies.    Am.  Inst.  Elec. 

Eng.,  Sept.  25,  1903. 

18.  Crowell,  H.  C.  and  Lenth,  G.  C.  D.     An  Investigation  of  the  Doble  Needle 

Regulating  Nozzle.     Thesis,  Mass.  Inst.  of  Tech.     1903. 

19.  LeConte,  Joseph  N.     Efficiency  Test  of  an  Impulse  Wheel.     Cal.  Jour,  of 

Tech.     May,  1904. 

20.  Groat,  B.  F.     Experiments  and  Formula  for  the  Efficiency  of  Tangential 

Water  Wheels.     Eng.  News,  1904,  vol.  2,  p.  430. 

21.  Webber,  Wm.  0.     Efficiency  Tests  of  Turbine  Water  Wheels.     Am.  Soc. 

of  Mech.  Engrs.,  May,  1906. 

22.  Horton,  R.  E.     Turbine  Water  Wheel  Tests.     Water  Supply  and  Irriga- 

tion Paper  180,  1906. 

23.  Westcott,  A.  L.     Tests  of  a  12-inch  Doble  Water  Wheel.     Power,  Dec. 

1907. 


CHAPTER  XVI. 

THE  SELECTION  OF  THE  TURBINE. 

182.  Effect  of  Conditions  of  Operation. — For  high  and  moder- 
ate falls  the  variations  in  head  under  different  conditions  of  flow 
are  of  small  importance  and  water  wheels  can  commonly  be 
placed  high  enough  above  tail-water  to  be  practically  free  from 
its  influences.  In  such  cases  variations  in  head  are  comparatively 
so  slight  as  to  have  little  effect  on  the  operation  of  the  wheels 
which  can  therefore  be  selected  for  a  single  head.  Such  condi- 
tions are  the  most  favorable  for  all  types  of  wheels. 

When  low  falls  are  developed  the  rise  in  the  tail-water  is  often 
comparatively  great,  and,  as  the  head  water  cannot  commonly 
be  permitted  to  rise  to  a  similar  extent  on  account  of  overflow 
and  damage  from  back  water,  the  heads  at  such  time  are  consider- 
ably reduced.  As  is  pointed  out  in  Chapter  V,  under  such  con- 
ditions and  for  continuous  power  purposes  wheels  must  be  se- 
lected, if  possible,  that  will  operate  satisfactorily  under  the  entire 
range  of  head  variations  that  the  conditions  may  demand,  or  at 
least  under  as  great  a  range  of  such  variations  as  practicable. 

In  some  cases  the  change  in  head  is  so  great  that  no  wheel  can 
be  selected  which  will  work  satisfactorily  under  the  entire  range 
of  conditions.  In  other  cases,  the  head  becomes  so  small  that 
the  power  which  can  be  developed  is  insufficient  without  a  large 
and  unwarranted  first  cost.  In  many  such  cases  the  use  of  the 
water  power  plant  must  be  discontinued,  and,  if  the  delivery  of 
power  must  be  continuous,  it  must  be  temporarily  supplemented 
or  replaced  by  some  form  of  auxiliary  power. 

In  Chapter  XVII  it  is  shown  that,  almost  without  exception, 
great  variations  take  place  in  every  power  load  and  that  a  plant 
must  therefore  be  designed  to  work  satisfactorily  under  consider- 
able changes  in  load.  Most  plants  are  called  upon  to  furnish 
power  for  a  considerable  portion  of  the  time  under  much  less 
than  their  maximum  load,  but  must  occasionally  furnish  a  maxi- 
mum load  for  a  short  period. 


Basis  tor  the  Selection  of  the  Turbine.  385 

If  power  is  valuable,  and  the  quantity  of  water  is  limited,  it  is 
•desirable  to  select  a  wheel  that  will  give  the  maximum  efficiency 
for  the  condition  of  load  under  which  it  must  operate  for  the 
.greater  portion  of  the  time  and  that  will  also  give,  if  possible, 
high  efficiency  under  the  head  available  at  the  lowest  stages  of 
the  water.  High  efficiency  is  not  essential  to  economy  during 
high  water,  for  there  is  plenty  of  water  to  spare  at  such  times; 
neither  is  high  efficiency  as  important  during  unusual  load  con- 
ditions, which  obtain  for  only  brief  intervals,  as  it  is  during  the 
average  conditions  under  which  the  plant  operates. 

183.  Basis  for  the  Selection  of.  the  Turbine.— In  Chapter  XV 
the  testing  of  water  wheels  has  been  discussed  and  a  number  of 
tabulated  results  of  such  tests  are  given.  (See  appendix  D).  The 
•standard  water  wheel  tables  are  calculated  from  the  results  of 
these  tests  but  the  values  of  power  and  efficiency,  as  given  therein, 
are  usually  reduced  somewhat  for  safety  from  the  results  deter- 
mined experimentally.  Such  tests  also  give  data  for  a  much 
broader  consideration  of  the  question,  and  for  the  determination 
•of  the  results  that  can  be  obtained  under  the  actual  conditions 
•of  installation  and  operation,  even  when  such  conditions  are  sub- 
ject to  wide  variations. 

In  Chapter  XIV  the  hydraulics  of  the  turbine  are  discussed, 
various  turbine  constants  are  considered,  and  the  constants  are 
calculated  for  a  number  of  standard  American  turbines  in  accord- 
ance with  the  conditions  of  operation  as  recommended  in  the  -cata- 
logues of  their  makers.  It  will  be  seen  from  a  study  of  the  tables 
that  the  turbines  designed  and  built  by  various  manufacturers 
sometimes  have  widely  different  constants,  indicating  that  each  is 
best  adapted  to  certain  conditions  of  which  the  values  of  these 
•constants  are  an  index. 

It  is  also  shown  that  the  various  constants  for  a  homogeneous 
•series  of  wheels  may  be  calculated  from  experimental  data  for 
any  desired  condition  of  gate  opening  and  fixed  value  of  <j>,  and 
that  from  these  constants  the  operating  results,  that  is,  the  dis- 
charge, power,  speed,  and  efficiency  for  any  wheel  of  the  series, 
with  the  given  gate  opening  and  value  of  (f>  and  for  any  desired 
head,  can  be  calculated.  For  most  purposes,  where  the  head  is 
•constant  or  where  the  range  in  heads  and  other  conditions  to  be 
considered  are  not  extreme,  the  necessary  calculations  can  be 
readily  made  from  a  satisfactory  test,  by  applying  some  of  the 


38£  The  Selection  of  the  Turbine. 

formulas  developed  and  discussed  in  Chapter  XIV.     The  formu- 
las of  greatest  value  for  this  purpose  are  as  follows: 


^  ^  P  n 


1842  cp 

2  Hi=  — jr — ,  when  h  =  1 

D  n  _  D,    nt 

3  A  =  •  / .  —  — /—  •     when  cp  is  constant. 

v  h  V  h , 

4  /— :  =  "  /-—     when  q>  and  D  are  constant. 
Vh         1/h, 

5  n  =  n,  Vh     when  (p  and  D  are  constant. 


7          —7=  =  -7=    when  cp  and  D  are  constant. 

Vh       Vh,  ^  «> 

g  q  =  q,  Vh      when  (p  and  D  are  constant. 

P  PI 

9  K2  =• ~  =  TTn — 7"    when  (p  is  constant. 

D*  h£          DI  hjk 

P  PI 

10  -  3    =  3     when  (p  is  constant. 

p  _  p  iva      when  <^  and  D  are  constant  and  hi  =  1. 
12 

In  using  these  formulas  it  must  be  remembered  that  each  is 
essentially  correct  only  when  the  condition  specified  after  each 
equation  obtains ;  also  that  as  long  as  </>  remains  constant  the 
efficiency  obtained  by  the  test  will  remain  practically  constant 
for  the  same  wheel,  under  all  conditions  of  head.  It  should  also 
be  noted  that,  with  a  fixed  diameter  of  wheel  and  a  fixed  head,  <f> 
and  n  are  in  direct  proportion,  and  most  calculations  can  be  made 
by  a  direct  consideration  of  the  values  cf  n  without  a  determina- 
tion of  the  value  of  <f>. 

When  the  operating  results  are  calculated  for  a  wheel  of  a  given 
series  but  of  a  diameter  differing  from  that  on  which  the  experi- 
ments were  made,  the  results  are  liable  to  differ  from  the  true 
results  on  account  of  variations  in  manufacture,  and  allowance 
must  be  made  for  such  differences,  at  least  until  the  art  of  manu- 
facturing turbines  has  further  advanced. 


Selection  of  the  Turbine  for  Uniform  Head  387 

184.  Selection  of  the  Turbine  for  Uniform  Head  and  Power. — 

The  conditions  of  operation,  as  catalogued,  are  usually  based  upon 
tests  of  a  few  turbines  of  the  series,  and  represent  the  best  con- 
ditions of  operation  for  that  series  of  wheels  as  determined  by 
such  tests.  Where  the  conditions  of  installation  and  operation 
are  fixed,  and  are  not  subject  to  radical  changes  in  head  or  to  great 
variations  in  the  demand  for  power,  the  selection  of  a  wheel  may 
be  made  by  inspection  directly  from  the  catalogues.  This  method 
of  selection  is  based  on  the  assumption  that  the  catalogue  data  is 
correct,  which  assumption  should  be  verified  by  the  records  of 
an  actual  test  of  the  series  of  wheels  and,  if  possible,  of  the  size 
and  hand  which  are  actually  to  be  used. 

The  examination  of  the  many  catalogues  of  turbine  manufactur- 
ers, in  order  to  determine  the  wheel  best  suited  to  the  conditions, 
is  a  tedious  method  of  procedure  and  can  be  greatly  shortened  by 
brief  calculations  which  are  described  in  the  following  sections : 

185.  The  Selection  of  a  Turbine  for  a  Given  Speed  and  Power 
to  Work  under  a  Given  Fixed  Head. — It  is  frequently  necessary 
to  select  a  turbine  which  must  have  a  given  speed  and  power  in 
order  to  successfully  operate  machinery  for  w1iich   such  require- 
ments obtain.     It  is  desirable  to  select  a  wheel  which  will  furnish 
essentially  the   amount   of  power   required   as   all   machinery   will 
work  more  efficiently  and  more  satisfactorily  at  or  near  full  load 
conditions.     It  is  also  desirable  to  use  a  single  turbine  rather  than 
two  turbines,  and  if  more  than  one  turbine  is  required,  the  least 
number  found  practicable  should  usually  be  selected  because  the 
multiplication  of  units  involves  an  increase  in  the  number  of  bear- 
ings which  must  be  maintained  and  kept  in  alignment. 

To  determine  the  best  installation  of  turbines  necessary  to  ful- 
fill the  given  conditions,  the  value  of  K5  as  given  by  equation  (12) 
should  be  determined.  Having  determined  the  value  of  K5,  a 
turbine  should  be  selected  having  a  constant  K5  not  less  than  the 
amount  determined,  and  if  it  is  desired  to  operate  the  turbine  at 
its  maximum  efficiency,  the  value  of  K5  for  the  turbine  selected 
should  not  greatly  exceed  the  value  found  by  computation.  If 
the  value  of  K5  as  computed  greatly  exceeds  the  value  of  K5  for 
the  various  makes  of  turbines,  then  the  power  must  be  divided 
between  two  or  more  units  in  order  that  the  conditions  may  be 
satisfied.  As  K5  is  in  direct  proportion  to  P,  one-half,  one-third  or 
any  other  fraction  of  K3  will  give  the  value  of  K5  for  a  wheel 
having  a  similar  fractional  value  of  the  power,  P,  and  will  there- 


388  The  Selection  of  the  Turbine. 

fore  show  the  type  of  wheel  which'  must  be  selected  in  order  that 
two,  three,  or  more  will  do  the  work  in  question.  The  great  varia- 
tions in  the  value  of  K5  for  different  types  of  wheels  and  the  in- 
fluence of  this  variation  on  the  relation  of  speed  and  power  will 
be  seen  by  reference  to  Fig.  222  which  shows  the  curves  of  re- 
lation between  revolution  and  power  of  various  wheels  for  one 
foot  head.  This  may  be  used  for  any  other  head  by  considering  the 
revolutions  in  proportion  to  the  square  root  of  the  head  and  the 
power  in  proportion  to  the  three-halves  power  of  the  head.  A 
brief  study  of  this  diagram  will  show  its  use  more  plainly.  For 
example  :  under  a  one  foot  head,  and  for  30  revolutions  per  minute, 
turbines  may  be  selected  that  will  deliver  from  1.3  to  6.6  horse 
power. 

Suppose  we  desire  to  determine  the  power  that  will  be  available 
under  a  16'  head  at  100  revolutions  per  minute.  100  revolutions 
per  minute  at  16'  head  would  correspond  to  25  revolutions  per 
minute  at  i'  head. 

For  since 


n    =  -7=5=1 

Vh> 

vr 

therefore  n1  =  -j=  100  =  .25  X  100  =  25. 
V10 

At  25  r.  p.  m.  the  diagram  shows  that  turbines  are  obtainable 
that  will  give  1.8  to  10  horse  power  at  one  foot  head. 

The  power  at  16  foot  head  will  be  to  the  power  at  one  foot  head 
as  the  three-halves  power  of  the  head.  The  three-halves  power  of 
16  is  64;  hence  the  power  at  16  feet  will  be  64  times  the  power  at 
ooie  foot  head,  and,  hence,  wheels  under  a  16  foot  head  operated  at 
100  revolutions  per  minute,  will  furnish  from  122  to  657  horse 
power  and  the  most  satisfactory  wheel  within  these  limits  for  the 
problem  at  hand  can  be  selected. 

The  diagram,  however,  is  a  convenience,  not  a  necessity,  and  a 
problem  can  often  be  more  readily  solved  by  the  direct  applica- 
tion of  equation  12.  If,  for  example,  it  is  desired  to  operate  a 
turbine  at  100  revolutions  per  minute  under  16  foot  head  to  de- 
velop 400  h.  p.,  the  corresponding  value  of  K5  will  be 

nap        100  X  100  X  400 


By  examination  of  Table  XXXII  it  will  be  found  that  the  Victor 
Standard  Cylinder  Gate  or  the  United  States  Turbine  wheels  have 


To  Estimate  Probable  Results  From  a  Test.  389 

practically  this  value  of  K5  and  will  therefore  fulfill  the  conditions. 
Having  determined  from  the  calculated  value  of  K5  the  makes  and 
types  of  the  several  wheels  which  will  satisfy  the  requirements,  the 
size  of  the  wheel  may  immdiately  be  determined  by  determining 
the  value  >of  K2  for  the  same  series  of  wheels  from  Table  XXX, 
Chap.  XIV,  and  calculating  the  size  of  the  wheel  by  the  use  of  for- 
mula 9. 

Thus  for  the  Victor  Standard  Cylinder  Gate  wheel  the  value  of 
K2  is  0.00205.  Therefore  from  equation  (9) 

D  *  *pLl  *    JZIJ?OII  =  55,2' 
VK2  h|        ^.00205  X  64 

which  is  the  size  of  this  series  of  wheels  needed  to  fulfill  the  as- 
sumed conditions. 

Having  thus  selected  several  possible  wheels,  tenders  for  these 
wheels  may  be  invited  from  their  makers.  These  tenders  should 
be  accompanied  by  an  official  report  of  a  Holyoke  test  for  the 
wheel  in  question,  or,  if  this  is  not  available  at  the  time,  for  the 
next  larger  and  the  next  smaller  wheels  of  the  series  which  have 
been  tested.  From  these  tests  the  catalogue  values  of  K2  and  K5 
which  were  used  in  their  selection  can  be  checked.  In  addition 
to  this  the  several  prospective  wheels  may  be  compared  as  to  their 
operation  at  part  gate,  which  comparison  is  equally  important 
for  the  final  choice  to  be  made. 

As  the  wheels  are  seldom  or  never  tested  for  the  head  under 
which  they  are  to  work,  and  as  tests  are  not  always  available  for 
the  size  of  wheel  to  be  used,  it  is  necessary  to  predict  from  the  test 
data  furnished  by  the  wheel  makers  the  efficiency,  power  and 
water-consumption  curves  which  can  be  anticipated  under  the 
given  head.  This  can  be  done  as  illustrated  in  the  next  two 
articles. 

1 86.  To  Estimate  the  Operating  Results  of  a  Turbine  under 
one  Head  from  Test  Results  secured  at  another  Head. — For  the 
purpose  of  illustrating  the  methods  of  calculation,  Table  l-XX  tit 
may  be  considered.  This  table  gives  the  results  of  certain  tests 
of  a  33"  special,  left-hand  turbine  wheel,  with  conical  draft  tube 
and  balance  gate,  manufactured  by  the  S.  Morgan  Smith  Com- 
pany. While  the  heads  in  the  different  experiments  of  this  test 
vary  slightly,  they  are  so  nearly  uniform  that  the  table  may  be 
considered  as  developed  under  a  uniform  head  of  17.15  feet.  If 
greater  accuracy  is  desired,  however,  the  square  root  of  the  actual 
head  can  be  considered  each  time. 


39°  The  Selection  of  the  Turbine. 

Let  it  be  assumed  that  the  wheel  is  to  be  operated  under  a  20 
foot  head  and  with  a  speed*  of  200  r.  p.  m.  with  the  average  load 
at  about  .75  gate.  The  maximum  efficiency  at  .75  gate  is  repre- 
sented by  experiment  No.  43  of  this  table.  In  order  that  the 
wheel  shall  work  under  the  new  head  with  this  efficiency,  equation 
(4)  must  be  satisfied.  In  all  of  these  equations  the  primed  char- 
acters are  used  to  represent  the  experimental  conditions.  The 
most  efficient  revolutions  under  the  new  head  will  therefore  be 
determined  as  follows  : 

172.75  X  4.46 
n  =  4  14  =  186  r.  p.  m. 

The  wheel  to  be  chosen  must,  however,  in  this  case  operate  at 
200  revolutions  per  minute.  At  200  r.  p.  m.  the  wheel  will  not 
run  at  its  maximum  efficiency.  The  actual  efficiency  at  this  speed 
may  be  determined  by  finding  what  speed  at  the  experimental 
head  corresponds  with  the  speed  to  be  used,  and  noting  the  effi- 
ciency corresponding  to  the  same.  This  is  done  on  the  assump- 
tion that  the  efficiency  remains  constant  as  long  as  <j>  remains 
constant  which  is  shown  to  be  essentially  true  by  Fig.  214,  Chap. 
XIV. 

The  revolutions  under  17.16  ft.  head  corresponding  to  200  r. 
p.  m.  under  20  feet  will  be  determined  as  before  : 

2GO  x  4.14 
n    : 


4.4(5  -     -      . 

The  result,  187  r.  p.  m.,  lies  between  the  conditions  of  experi- 
ments 41  and  40.  By  proportion,  the  efficiency  corresponding  to 
187  r.  p.  m.  will  be  found  to  be  about  83.25  at  .75  Jgate. 

If  the  efficiency  corresponding  to  187  r.  p.  m.  in  the  table  is  now 
determined  from  each  gate  opening,  it  will  be  found  that  at  full  gate 
the  efficiency  will  be  slightly  below  that  shown  in  experiment  16, 
and  can  be  determined  by  interpolation,  or  graphically,  to  be 
about  81%.  At  gate  .9448  the  efficiency  can  be  determined  in  the 
same  way  to  be  about  82.75%.  At  gate  .883  the  results  will  fall 
between  experiments  69  and  70  and  the  efficiency  will  be  found  to 
be  about  86%.  At  gate  .851  the  result  falls  below  experiment  54,. 
and,  by  calculation  from  a  graphical  diagram  or  by  interpolation, 
the  results  are  found  to  be  about  .86.  At  gate  .702  the  revolutions 
correspond  exactly  with  experiment  56,  and  the  efficiency  from  the 
table  is  found  to  be  81.01%.  At  gate  .636  the  revolutions  fall  be- 
tween experiments  24  and  25  and,  by  proportion,  the  efficiency  is 


Effects  of  Diameter  on  Results. 


391 


found  to  be  80.25%.  At  gate  .556,  the  efficiency  is  found,  by  pro- 
portion, to  be  77%.  To  determine  the  power  of  the  wheel  under 
the  new  conditions,  and  for  each  condition  of  gate,  the  power  of 
the  wheel  as  found  by  the  test  must  be  determined  for  the  same 
value  of  $.  The  power  of  the  new  head  can  then  be  calculated  by 
\ise  of  formula  (n). 

In  the  same  manner  the  discharge  of  the  turbine  can  be  deter- 
mined by  finding  the  value  of  q  corresponding  to  the  value  of  <f> 
for  the  experimental  head,  and  from  this  value  so  determined  the 
value  of  q  under  the  20  foot  head  can  be  calculated  by  formula  (7). 
The  results  of  these  calculations,  together  with  the  efficiency  as 
determined  for  20  foot  head  and  for  200  revolutions  per  minute, 
are  given  in  Table  XXXVII. 

Having  computed  a  similar  table  for  each  of  the  several  pros- 
pective wheels  the  one  best  suited  to  the  given  conditions  can  be 
•chosen. 

TABLE  XXXVII. 

Showing  Horse  Power,  Discharge  and  Efficiency  of  33-inch  Special  Left  Hand 
S.  Morgan  Smith  Turbine,  with  20-foot  head  and  200  R.  P.  M. 

Calculated  from  test  of  33-inch  wheel  under  a  head  of  17.15  feet. 


Proportional  Gate  Opening. 

Horse  Power 

Discharge, 
cubic  feet 
per  second. 

Efficiency. 

1  COO                   .       .       

222.1 

120.4 

81.6 

.948    

•>•>$  .  1 

117.0 

83.2 

.883  

217.7 

111.3 

85.6 

.851  

212.7 

100.2 

86.3 

76o 

188  I 

97  5 

83.2 

702 

1(>5  1 

87.8 

81.3 

.636 

154.7 

81.5 

80.7 

55  1>                                                         .    . 

136.7 

75.0 

79.0 

187.  To  Estimate  the  Operating  Results  of  a  Turbine  of  one 
Diameter  from  Test  Results  of  Another  Diameter  of  the  Same 
Series.— It  is  always  desirable  for  the  purpose  of  calculations  to 
use  the  results  of  a  test  made  on  a  wheel  of  the  same  size  and  hand 
as  that  which  is  to  be  used  in  the  installation  for  which  the  wheel 
is  being  considered.  It  is  seldom,  however,  that  all  of  the  various 
sizes  of  wheels  in  a  series  of  wheels  have  been  tested,  and  the 
manufacturers  therefore  frequently  base  their  estimates  and  guar- 
•antees  of  wheels  of  an  untested  size  on  the  test  of  some  other 
wheel  of  the  series  which  may  be  larger  or  smaller  than  the  wheel 


392  The  Selection  of  the  Turbine. 

offered.  Sometimes  tests  of  wheels  both  larger  and  smaller  than 
the  wheel  to  be  used  are  available,  in  which  case  both  sets  of  tests 
should  be  used  as  a  basis  of  calculation. 

Let  it  be  assumed  that  a  40"  wheel  is  to  be  installed  of  the -same 
series  as  the  33"  wheel  just  considered,  and  that  no  tests  of  such 
a  wheel  are  obtainable.  The  tests  of  the  33"  wheel  may  therefore 
be  used  as  the  best  information  available.  Let  it  be  assumed  that 
the  40"  wheel  is  to  be  operated  under  a  9  foot  head-.  For  these- 
calculations  formula  (3)  must  be  satisfied. 

Let  it  be  assumed  that  the  wheel  is  to  operate  at  nearly  full  load* 
and  the  best  efficiency  is  desired  at  about  .85  gate.  From  the1  tests  it 
will  be  found  that  at  .85  gate,  and  with  a  17.15  foot  head  and  191 
revolutions,  the  wheel  gave  85.97%  efficiency  and  170.08  horse 
power.  Substituting  these  values  in  equation  (3)  there  results : 

33  X  191          40  X  n 

— T~T7 —     — o )  from  which  n  =  114  r.  p.  m. 

One  hundred  and  fourteen  revolutions  per  minute  is  therefore 
the  speed  under  which  the  wheel  must  operate  in  order  to  give 
this  maximum  efficiency  at  this  gate. 

Let  it  be  assumed,  however,  that  the  wheel  must  be  run  at  120 
r.  p.  m.,  on  account  of  the  class  of  machinery  to  be  operated 
By  substituting  the  value  n=J2O,  in  equation  (3),  it  is  found 
that  n'=2O2.  The  experimental  efficiency  at  202  r.  p.  m.  under 
the  I7-J5  foot  head  and  with  the  33"  wheel,  will  therefore,  corres- 
pond to  120  revolutions  under  a  9  foot  head  with  a  40"  wheel,  and 
will  indicate  the  efficiency  under  which  the  wheel  will  operate  under 
these  conditions.  This  is  found  to  be  about  81.5  at  .85  gate. 

In  order  to  determine  the  horse  power  of  the  wheel  under  the 
new  conditions,  the  horse  power  of  the  wheel  under  the  test  con- 
ditions must  first  be  determined  for  that  gate;  the  resulting  horse 
power  can  then  be  determined  by  equation  (9). 

For  202  r.  p.  m.  at  17.15  foot  head  for  this  33'  wheel  P=158- 
which,  substituted  in  equation  (9),  gives 

158  P 

33  X  33  X  71       =  40  X  40  X  27  from  which  P  =  88« 

Jn  the  same  manner,  the  discharge  of  the  larger  wheel  under  the 
lower  head  can  be  determined  by  equation  (6),  and  q  is  found  ta 
equal  104  cu.  ft.  per  second. 


To  Estimate  Results  with  Variable  Heads. 


393 


In  this  way  the  discharge,  efficiency  and  power  of  the  larger 
wheel  under  the  chosen  r.  p.  m.  can  be  determined  for  each  condi- 
tion of  gate,  as  shown  in  Table  XXXVIII. 

TABLE  XXXVIII. 

Showing  Horse  Power,  Discharge  and  Efficiency  of  a  40-inch  Special  Left  Hand 

S.  Morgan  Smith  Turbine,  with  a  9-Joot  hea  i  and  120  R.  P.  M. 

Calculated  from  test  of  33-inch  wheel  under  a  head  of  17.15  feet. 


Proportional  Gate  Opening. 

Horse 
Power 

Discharge 
cubic  feet 
per  second. 

Efficiency. 

1  000                              

100 

119 

8'?  1 

948    .           

100 

112 

84  2 

.883    

92 

108 

82  5 

.851  

88 

104 

81  5 

.765  

76. 

91. 

78.1 

70? 

68 

83 

77  8 

.«36  

64. 

76. 

78.8 

.550  

58 

73 

75  1 

1 88.  To  Estimate  the  Operating  Results  of  a  Turbine  under 
Variable  Heads  from  a  Test  made  under  a  Fixed  Head. — Where 
the  variations  in  the  head  under  which  a  wheel  is  to  operate  are 
considerable,  the  variation  in  <£,  and  consequently  in  n,  are  some- 
times found  to  be  beyond  the  limits  of  the  test.  Where  the  test 
conditions  are  not  greatly  exceeded,  the  experiments  may  be  ex- 
tended graphically  without  any  serious  error. 

Let  it  be  assumed  that  the  33"  wheel  above  considered  is  to  be 
operated  under  a  maximum  head  of  25  feet,  and  that  the  head  will 
decrease  to  16  feet  at  times  of  high  water;  also,  that  the  wheel  is 
to  be  operated  for  the  major  portion  of  the  time  under  about  .75 
gate.  The  best  condition  for  operation  is  shown  by  test  43,  which 
shows  an  efficiency  of  86.3%  at  n' =  172.75  r.  p.  m. 

n  may  be  calculated  from  equation  (4)  for  the  25  foot  head  as 
follows : 


n  = 


172.75  X  5 
4.14 


=  208  r.  p.  m. 


That  is :  the  best  number  of  revolutions  for  a  25  ft.  working  head 
would  be  207  r.  p.  m.  The  best  number  of  revolutions  for  a  six- 
teen foot  head  would  be  determined  as  follows : 


n  = 


172.75  X  4 
4.14 


=  166  r.  p.  m. 


24 


394  The  Selection  of  the  Turbine. 

The  wheel,  for  the  best  efficiency,  should  be  run  at  a  different 
speed  for  each  head,  but  under  practical  conditions  of  service 
must  be  run  at  a  constant  speed. 

Let  it  be  assumed  that,  on  account  of  the  machinery  operated, 
it  is  desirable  to  adopt  for  the  plant  a  speed  of  200  r.  p.  m.  Let 
the  25  foot  head  be  first  considered.  For  considering  the  25  foot 
head  the  equivalent  value  of  n  under  the  test  conditions  is  found 
as  follows: 


=167r.p.m. 


It  will  be  noted  from  experiment  44  that  at  169.25  r.  p.  m.  the 
efficiency  is  85.55.  At  167  revolutions  per  minute  the  efficiency 
would  therefore  be  about  85%.  Under  a  sixteen  foot  head  n  must 
also  equal  200  r.  p.  m.,  hence,  for  this  case,  the  equivalent  value  of 
n'  for  the  test  conditions  is 

n'=   200X4.14    =  20S  revoh.tions. 

Test  39  shows  that,  with  206.25  revolutions,  the  efficiency  is 
76.66.  At  208  revolutions  the  efficiency  is  therefore  less  than  this 
amount  and  the  probable  efficiency  under  these  conditions  can 
be  estimated  by  platting  the  relation  between  revolutions  and  ef- 
ficiency as  shown  in  Fig.  238.  By  prolonging  the  line  from  the 
actual  experiments,  the  efficiency  indicated  for  208  revolutions, 
under  the  experimental  conditions,  is  found  to  be  about  76%. 
As  far  as  efficiency  is  concerned,  therefore,  the  arrangement  is  very 
satisfactory,  for  a  sufficiently  high  efficiency  will  be  obtained  un- 
der conditions  of  high  water,  and  when  the  quantity  of  water  used 
is  immaterial. 

The  relations  of  efficiency  to  speed,  under  the  experimental  con- 
ditions and  at  various  gate  openings,  are  shown  by  the  points 
platted  on  Fig.  238.  Through  these  points  mean  curves  are 
drawn,  which  are  extended  where  necessary  to  intersect  the  ab- 
scissa of  167  revolutions,  which  corresponds  to  the  condition  of 
efficiency  for  25  foot  head,  and  to  the  abscissa  of  208  revolutions, 
which  corresponds  to  the  condition  of  efficiency  for  a  16  foot  head. 
From  these  results  the  relations  of  efficiency  at  various  gates  and 
at  the  two  heads  named  are  platted  in  Fig.  239. 

The  relations  of  power  to  speed  are  shown  by  Fig.  240,  which 
has  been  platted  in  the  same  manner  as  Fig.  238.  From  Fig.  240; 


Estimate  of  Efficiency  with  Variable   Head. 


395 


..-_  ISO  BOO  _«., 

RC VOLUTIONS    PER    Ml  MUTE. 

Fig.  238. — Curves  Showing  the  Efficiency  Obtained  at  Various  Speeds  un- 
der a  Test  Head  of  about  17.15  Feet  from  a  33-Inch  Special  Left- 
Hand  Wheel  with  Balance  Gate,  Manufactured  by  the  S.  Morgan 
Smith  Co. 


70 


50 


60 


70          80 
PER  CENT  GATE  OPENING. 


90 


Fig.  239.— Curves  Showing  Estimated  Efficiency  at  Various  Gate  Openings 
and  at  Two  Heads  for  33-Inch  S.  Morgan  Smith  Wheel.  (Taken 
from  Fig.  238.) 


396 


The  Selection  of  the  Turbine. 


the  power  of  the  wheel  at  25  and  16  feet  can  be  determined  by 
equation  (10). 

The  power  at  25  feet  will  be 


125 


j  =  =g-g  =  l .  77  times  the  power  determined  by  the  exper- 

h'*  iment  at  17.15  feet  and  167  r.  p.  m. 


The  power  at  16  feet  will  be 


64 

—  =  ;=7r~7:  =  .91  times  the  power,  as  determined  by  the  ex- 
periment at  17.15  feet,  and  at  216  r.  p.  m. 


180 


I  DO 


180 
REVOLUTIONS  PER  MINUTE 


HDD 


220 


Fig.  240. — Curves  Showing  the  Power  Obtained  at  Different  Speeds  under  a 
Test  Head  of  about  17.15  Feet  from  the  S.  Morgan  Smith 
33-Inch  Wheel. 

.91  times  the  power,  as  determined  by  the  experiment  at  17.15  feet, 
and  at  216  r.  p.  m.  Curves  of  the  powrer  of  this  wheel  under  25  and 
1 6  foot  heads,  and  at  various  gates,  as  determined  in  this  manner, 
are  shown  by  Fig.  241. 

The  experimental  relations  of  speed  and  discharge  for  the  wheel 
are  shown  in  Fig.  242  which  was  platted  in  the  same  manner  as 
the  diagrams  for  efficiency  and  power.  A  graphical  representa- 
tion of  the  discharge  under  25  and  16  foot  head  and  at  various 
gates  is  shown  in  Fig.  243. 

189.  A    More    Exact    Graphical    Method    for    Calculation. — The 
method  outlined  in  section  188  is  subject  to  some  error  as  the  re- 
sults are  platted  regardless  of  head.     The   graphical   method   is 
therefore  applicable  without  correction  only  when  the  experimen- 


A  Graphical  Method  of  Calculation. 


397 


tal  head  remains  nearly  constant.  For  a  more  complete,  accurate 
and  satisfactory  analysis  the  discharge,  power  and  revolutions 
should  be  reduced  to  their  equivalents  i.  e.  at  one  foot  head 

JL   P   .    _L.   h         * 

41        Vh,  hi  Vh 


300 


260 


J220 


80 


140 


100 


GO 


70 
CENT 


OPENING. 


90 


1QD 


PER    CENT    GATE 

Tig.    241. — Curves    Showing    Estimated    Power    Obtained    at    Various    Gate 

Openings  and  at  Two  Heads  for  33-Inch  S.  Morgan  Smith  Wheel. 

(Taken  from  Fig.  240'.) 

and  platted  as  shown  in  Fig.  244  where  the  r.  p.  m.  under  one  foot 
head  is  used  as  abscissas,  and  the  power,  discharge  and  efficiencies 
are  used  as  ordinates.  The*  condition  at  any  given  number  of 
revolutions  under  a  given  head  can  be  calculated  by  dividing  the 
given  number  of  revolutions  by  ttte  square  root  of  the  head.  The 


398 


The  Selection  of  the  Turbine. 


115 


160 


180  EDO 

REVOLUTIONS    PER    MINUTE 


220 


Fig.  242. — Curves  Showing  the  Discharge  at  Various  Speeds  under  the  Test 
Head  of  about  17.15  Feet  of  ths  33-Inch  S.  Morgan  Smith  Wheel. 


140 


120 


u  100 


5    BO 

u 
en 


60 


50 


60 


70  80 

PER     CENT     GATE     OPENING 


30 


100 


Fig.  243.— Curves  Showing  the  Estimated  Discharge  at  Various  Gate  Open- 
ings and  at  Two  Heads  for  the  33-Inch  S.  Morgan  Smith  Wheel. 
Taken  from  Fig.  242.) 


A  Graphical  Method  of  Calculation. 


399 


88! 


52  54 


36  38  40 

Fig.  244.— Curves  of  the  33-Inch  S.  Morgan  Smith  Wheel  for  One  Foot  Head. 


42  44  46  48  50 

R.P.M.  UNDER  ONE  FOOT   HEAD. 


400  The  Selection  of  the  Turbine. 

result  is  the  comparative  revolutions  under  one  foot  head,  and  a 
line  drawn  vertically  at  the  point  so  located  on  the  diagram  will 
.give  the  basis  of  calculations  for  power  and  discharge  by  multi- 
plying by  hi  and  ha,  respectively,  for  each  gate  opening  and  by 
reading  the  efficiency  direct. 

For  the  wheel  under  200  revolutions  at  25  and  16  foot  heads  the 
equivalent  speeds  on  the  diagram  are  40  and  50,  respectively, 
Lines  drawn  vertically  at  these  points  will  intersect  the  curves  of 
efficiency,  power  and  discharge  and  if  reduced  by  a  similar  method 
will  give  curves  essentially  the  same  as  those  shown  in  Figs.  239, 
241  and  243.  This  is  probably  the  best  method  for  common  use 
in  studying,  from  test  data,  the  operation  of  a  wheel  under  a  va- 
riable head. 

190.  The  Construction  of  the  Characteristic  Curves  of  a  Tur- 
bine.— It  is  frequently  desirable  to  make  a  more  thorough  analy- 
sis, based  on  the  available  test,  of  the  conditions  under  which  a 
•wheel  can  operate.  For  this  purpose,  the  writer  finds  the  use  of 
what  he  has  termed  "the  characteristic  curve"  of  a  turbine  to  be 
the  most  comprehensive  method  for  such  an  analysis. 

For  this  purpose,  prepare  a  diagram  on  which  the  ordinates  rep- 
resent the  values  of  <j>  and  the  r.  p.  in.  under  one  foot  head,  and 
the  abscissas  the  discharge  of  the  wheels  in  cubic  feet  per  second 
under  one  foot  head.  It  is  also  found  desirable  to  show  on  the 
upper  margin  of  the  diagram  the  horse  power  under  one  font  head 
with  100%  efficiency,  corresponding  to  the  discharge  shown  below. 
For  each  experimental  result  the  values  of  <j>  and  of  the  discharge 
under  one  foot  head  are  determined  by  formulas  (i)  and  (3). 
The  point  representing  these  values  is  then  platted  on  the  dia- 
gram, and  the  efficiency,  as  determined  by  the  test  for  that  experi- 
ment, is  written  closely  adjoining  the  platted  point.  This  is  done 
for  each  experiment  at  each  condition  of  gate.  After  all  the  ex- 
perimental points  are  platted,  and  the  resulting  efficiency  at  each 
given  point  is  expressed,  lines  of  equal  efficiency  are  interpolated 
on  the  drawing,  and  will  indicate  the  general  law  of  the  variation 
of  efficiency  as  represented  by  the  test. 

It  is,  of  course,  possible  to  reduce  the  horse  power  determined 
for  each  experiment  to  the  theoretical  horse  power  under  one  foot 
head,  and  record  it  at  the  corresponding  point,  and  then  interpolate 
horse  power  curves,  as  in  the  case  of  the  efficiency  curves.  It  has 
been  found  by  the  writer,  however,  to  be  more  satisfactory  to  use 


The  Characteristic  Curve.  401 

the  horse  power  scale  at  the  top  of  the  diagram,  together  with  the 
efficiency  lines  already  drawn,  for  the  calculation  and  platting  of 
the  horse  power  curves.  The  horse  power  at  any  point  will,  of 
course,  equal  the  theoretical  horse  power  expressed  at  the  upper 
margin,  multiplied  by  the  efficiency  at  the  given  points. 

In  determining  the  horse  power  curve,  it  is  best  to  assume  the 
horse  power  of  the  desired  curve,  and  then  determine  its  location 
in  regard  to  the  theoretical  horse  power  from  the  equation. 
A.  H.  P  =  T.  H.  P.  X  Efficiency. 

For  example,  on  Fig.  245,  if  it  is  desired  to  plat  the  curve  rep- 
resenting 2  A.  H.  P.  it  may  be  done  as  follows : — The  line  repre- 
senting two  actual  horse  power  will  intersect  the  70%  efficiency 
line  at  two  points  whose  abscissae  are  determined  from  the  T.  H. 
P.  scale  by  the  equation 

T.  n.  p.  = 

If,  therefore,  the  two  points  of  intersection  of  the  abscissa  2.86, 
as  indicated  on  the  upper  T.  H.  P.  scale,  with  the  70%  efficiency 
line,  are  marked,  two  points  will  be  established  on  the  2  A.  H.  P. 
line.  As  many  of  the  lines  of  equal  efficiency  and  equal  horse 
power  can  be  drawn  on  the  diagram  as  may  be  desired,  but  if  the 
lines  of  the  drawing  or  diagram  are  too  numerous,  confusion  will 
result  rather  than  clearness. 

One  of  the  most  complete  sets  of  experiments  with,  or  tests  of, 
a  turbine  water  wheel  which  the  writer  has  been  able  to  obtain 
is  the  set  of  experiments  made  for  the  Tremont  and  Suffolk  Mills 
at  the  Holyoke  Testing  Flume,  December  3-5,1890,  on  a  48  inch 
Victor  turbine,  with  cylinder  gate  (See  ''Notes  on  Water  Power 
Equipment,"  by  A.  H.  Hunking),  which  is  given  in  full  in  Table 
LX.* 

From  this  table,  and  in  the  manner  above  described,  a  char- 
acteristic curve  of  this  wheel  has  been  prepared,  and  is  shown  by 
Fig.  245.  In  this  Figure  the  efficiency  curves  are  shown  in  black, 
the  horse  power  curves  are  shown  in  red,  and  the  lines  showing 
the  relations  of  discharge  and  <j>  at  various  gate  openings  are 
shown  by  the  dotted  lines  connecting  the  experimental  points. 

191.  The  Consideration  of  the  Turbine  from  its  Characteristic 
Curve: — From  this  characteristic  curve  the  action  of  the  wheel 
under  all  conditions  of  operation  within  the  experimental  limits 
of  <f>  can  be  readily  determined.  The  use  of  the  characteristic 

*  See  Appendix — D. 


HORSE   POWER   UNDER   ONE  FOO 

.7       i.s      I.Q     e.a     s..\      s.z     2.3    a.**     e. 


so 


6  17  IB  |g         20         21  2 

DISCHARGE     IN      CUBIC       FEET     F 

Fig.  245. — "Characteristic  Curve"  of 


ME1AD   WITH   I  DO   PERCENT   EFFICIENCY 


23    S4    25    25    27    28    29    3D 
SECOND   UNDER   ONE   ROOT  MEAD 

18-Tnch  Victor  Turbine,  with  Cylinder  Gate. 


35         36 


404  The  Selection  of  the  Turbine. 

curve  is  based  upon  the  assumption  that  the  efficiency  will  remain 
constant  for  a  variable  head  as  long  as  4>  remains  constant. 

The  efficiency  and  horse  power  lines  as  interpolated,  are  sub- 
ject to  errors  of  interpolation,  the  extent  of  which  can  be  readily 
judged  from  the  diagram  made.  The  conditions  of  the  test  are 
approximately  checked  by  this  diagram,  for  any  marked  irregulari- 
ties in  these  curves  must  be  due  to  errors  in  testing,  or  to  poor 
workmanship. 

By  inspection  it  is  possible  to  decide  immediately  the  value 
of  <f>  that  must  be  maintained  in  order  to  maintain  the  maximum 
efficiency  at  any  particular  condition  of  gate.  For  example:  if 
the  maximum  efficiency  at  full  load  is  desired,  <£  with  this  wheel 
should  equal  about  .69.  If  the  maximum  efficiency  at  .75  gate  is 
desired,  the  value  of  <j>  should  be  about  .65,  and  for  maximum  ef- 
ficiency at  .50  gate,  <£  should  be  reduced  to  about  .64. 

Knowing  the  head  under  which  the  wheel  is  to  operate,  the  nec- 
essary number  of  revolutions  at  any  head  can  be  calculated  by 
formula  (i)  or  by  multiplying  the  r.  p.  m.  at  one  foot  head  by  the 
i/h  and  the  conditions  of  operation,  in  regard  to  both  power  and 
efficiency  at  all  gates,  will  be  determined  by  the  intersection  of  a 
horizontal  line  through  the  chosen  value  of  <£  with  the  efficiency 
and  horse  power  lines.  If,  for  example,  it  is  decided  that  $  shall 
be  .66,  a  horizontal  line  running  directly  through  the  diagram  at 
<£  =  .66  will,  by  means  of  the  various  points  of  intersection  with 
the  gate  opening,  efficiency  and  horse  power  lines,  give  all  infor- 
mation desired  and  from  it  can  be  calculated  the  efficiency,  speed, 
discharge  and  horse  power  of  the  wheel  for  the  head  under  which 
it  is  to  operate.  The  intersection  of  this  .66  </>  line  with  the  va- 
rious efficiency  curves  will  give  the  relation  of  efficiency  to  dis- 
charge with  one  foot  head.  The  discharge  under  the  required 
head  can  be  calculated  by  equation  (9),  i.  e.  by  multiplying  the  dis- 
charge shown  at  the  bottom  of  the  diagram  (cine  foot  head)  by  yh. 
The  efficiencies  at  each  gate  position  will  remain  unchanged  by 
this  change  in  head  since  <£  is  fixed  at  .66.  If  a  16  foot  head  be 
considered,  the  discharge  at  any  point  will  be  four  times  the  dis- 
charge read  from  the  diagram. 

The  relation  of  horse  power  to  discharge  is  aiso  shown  by  the 
intersection  of  the  <f>  line  with  the  horse  power  curves.  The  ac- 
tual horse  power  under  any  head  can  be  determined  by  equation 
(u)  i.  e.  by  multiplying  the  horse  power,  as  read  from  the  dia- 


The   Characteristic  Curve. 


.-gram  (one  foot  head)  by  h~.     The  horse  power  at  16  foot  head  will 
therefore  be  64  times  that  given  by  the  diagram. 

If  it  is  desired  to  utilize  the  characteristic  curve  for  the  consid- 
eration of  a  wheel  of  another  size  but  of  the  same  series,  the  power 

D  2 
.and  discharge  must  be  multiplied  by  the  ratio  -jj— 

All  of  the  various  types  of  curves  showing  the  results  of  opera- 


80 


40  GO  80  100 

DISCHARGE     IN     CUBIC      FEET      PER      SECOND   . 


120 


Fig.  246. 


406 


The  Selection  of  the  Turbine. 


tion  of  the  wheel  as  hitherto  described  are  shown  by,  or  can  be 
calculated  from,  the  characteristic  curve. 

Fig.  246,  showing  the  relation  of  the  number  of  revolutions  to  the 
efficiency  and  discharge  of  the  wheel,  is  one  example  of  such  use. 

192.  Other  Characteristic  Curves. — Fig.  247  is  the  characteristic 
curve  of  a  44  inch  "Improved  New  American"  turbine  showing  the 

HORSE    POWER    UNDER    ONE   FOOT    HEAD    WITH   100    PERCENT    EFFICIENCY 
2.0  2.5  3.0  3.5  4.0  4.5  5.0 


18     I*    20    22    24    26    28     30    32     34    36    38    40     42     44    46  4f~ 
DISCHARGE   IN   CUBIC   FEET  PER    SECOND   UNDER    ONE   FOOT    HEAD 

Fig.  247.— Characteristic  Curve  of  a  44-Inch  ""-Improved  New  American' 

Turbine. 


The  Characteristic  Curve. 


407 


operation  of  the  wheel  through  a  considerable  range  of  heads. 
The  outer  line  entitled  "Head  at  120  r.  p.  m.,  shows  the  values  of  <j> 
and  n-L  at  which  the  wheel  would  have  to  operate  to1  maintain  120 
r.  p.  m.  at  the  indicated  heads.  The  location  of  these  points  may 
be  determined  in  two  ways :  First. — By  calculating  the  values  of 


Fig.   248. — Curves  Constructed   from   Fig.   247   Showing  the   Power   at  Two 
Speeds  of  Six  "Improved  New  American"  Wheels. 


<f>  for  a  given  head  and  number  of  revolutions,  and  locating  the 
corresponding  point  from  the  scale  on  the  left  of  the  diagram; 
Second. — By  dividing  the  number  of  revolutions  by  the  square 
root  of  the  head  and  fixing  the  point  by  the  corresponding  revolu- 
tions under  one  foot  head,  as  shown  on  the  scale  of  r.  p.  m.  at  the 
right  of  the  diagram. 


408 


The  Selection  of  the  Turbine. 


At  14  foot  head  the  wheel  will  operate  at  about  the  maximum  ef- 
ficiency. If  the  head  be  decreased  to  12',  the  relative  efficiencies 
will  still  remain  fairly  satisfactory,  but  will  decrease  rapidly  at 
10'  as  shown  by  a  horizontal  line  drawn  through  the  corresponding 
point.  It  is  also  evident  that  at  8'  the  efficiency  becomes  very  low. 
and  below  this  head  the  wheel  would  probably  be  unable  to  main- 
tain 1 20  r.  p.  m. 

HORSE    POWER    UNDER    ONE   FOOT    HEAD   WITH    100    PERCENT    EFFICIENCY 
3.4          3.6  3.8  4.0          4.£  4.4          4.6  4.8          5.0  5.2  5.4          5.6  5.8 


DISCHARGE   IN   CUBIC  FEET  PER   SECOND   UNDER   ONE   FOOT    HEAD 


Fig.   249.— Characteristic  Curves  of  a  Wellman-Seaver-Morgan    51-Inch   Mc- 

Cormick  Wheel. 

The  second  line  at  the  right  shows  the  value  of  $  and  n,  at  va- 
rious heads  when  operating  at  100  revolutions  per  minute.  At 
this  speed  the  wheel  will  operate  satisfactorily  under  heads  from 
14'  to  as  low  as  7',  or  even  less.  The  efficiency  at  14  foot  head  in 
this  c'ase  will  be  less  than  at  120  r.  p.  m.,  and  the  efficiency  of  oper- 
ation will  increase  as  the  head  diminishes  to  the  9  and  10  foot' 
point,  where  the  best  efficiencies  are  obtained  at  100  r.  p.  m.  Be- 
low this  point  the  efficiency  of  operation  will  gradually  decrease. 
Provided  the  revolutions  per  minute  are  satisfactorily  selected,  it 
will  be  seen  that  the  wheel  will  meet  successfully  a  wide  variation 
in  the  operating  conditions. 


The  Characteristic  Curve. 


409 


Fig.  248  is  a  diagram  constructed  from  this  characteristic  curve 
and  shows  the  power  of  six  turbines  of  this  series  but  of  49"  diam- 
eter connected  tandem  to  a  horizontal  shaft  and  operated  at  the 
various  heads  and  revolutions  above  discussed.  The  curves  show 
the  condition  both  at  full  and  at  part  gates.  The  gradual  change 


145 


140 


HORSE  POWER  UNDER  ONE  FOOT  HEAD  WFTH  100  PERCENT  EFFICIENCY 
1.5      2.0.   .  .2.5.  .  .  ..-0 3.5.      4.0      4.5 5.0 


25 


10     12      14     16      18     20    22     24    26     28     30     32     34    36     38    40     4244 
DISCHARGE   IN   CUBIC   FEET  PER    SECOND   UNDER   ONE  FOOT    HEAD 


Fig.  250. — Characteristic  Curves  of  the  99i/,-Inch  Tremont  Fourneyron  Wheel. 


410 


The  Selection  of  the  Turbine. 


in  the  relative  position  of  the  100  and  the  120  r.  p.  m.  curves,  as 
the  head  changes,  should  be  noted. 

Fig,  249  shows  the  characteristic  curve  of  a  51"  McCormick  tur- 
bine, as  manufactured  by  Jolly  Brothers  for  the  Wellman-Seaver- 
Morgan  Company.  At  the  right  of  the  diagram  are  shown  the 
relative  values  of  <j>  and  at  the  left  the  values  of  n  for  heads  from 


HORSE    POWER    UNDER    ONE   FOOT    HEAD    WITH    100    PERCENT    EFFICIENCY 
83    26    27    38    29    30    31     32    33   34    35    36    37    38    39    40    4.1     43   43    44   45    4.6   4.7    48    49    , 


24     25     26     27      28     23      3D     .31      32      33     34      33     36      37      38      39     40     4       4Z     43     44    43 
DISCHARGE    IN    CUBIC    FEET  PER    SECOND    UNDER    ONE   FOOT    HEAD 

Fig.  251. — Characteristic  Curves  of  a  45-Inch  "Samson"  Wheel.     (James 

Leftel  &  Co.) 

16  to  8  feet,  at  90  and  100  r.  p.  m.  This  curve  shows  that  this 
wheel  will  work  satisfactorily  under  a  wide  range  of  conditions, 
if  a  suitable  speed  is  chosen. 

Fig.  250  is  the  characteristic  curve  of  the  Tremont  turbine  tested 
by  James  B.  Francis,  and  described  in  the  "Lowell  Hydraulic  Ex- 
periments." This  wheel  was  a  Fourneyron  turbine  of  about  700 
horse  power  at  13'  head. 

Fig.  251  is  the  characteristic  curve  of  a  45"  Leffel  turbine,  which 
has  been  selected  for  the  Morris  Plant  of  the  Economy  Light  and 
Power  Company,  now  under  construction  on  the  Des  Plainas 
River,  about  twelve  miles  south  of  Joliet,  Illinois.  It  is  to  be  op- 
erated at  120  revolutions  per  minute  and  under  variations  in  head 


The  Characteristic  Curve. 


411 


from  16  to  8  feet.  Eight  units,  each  consisting  of  .eight  of  these 
wheels,  connected  tandem,  are  to  be  installed  to  operate  eight  1,000 
K.  W.  alternating  generators.  This  diagram  was  prepared  from 
the  test  sheet  accompanying  the  bid  of  the  James  LefTel  &  Com- 
pany. In  the  construction  of  the  wheels  for  the  plant,  an  attempt 
was  made  to  so  alter  them  as  to  maintain  a  high  efficiency  for  a 


HORSE    POWER    UNDER    ONE   FOOT    HEAD   WITH    100    PER  CENT    EFFICIENCY 
2B  23          3.0          3.2          3.4          3.6          3.8          4.0          4.2          4.4          4.8          4.8          5.0          5.2 


26  28  30  32  34  36  38  40  42 

•DISCHARGE   IN   CUBIC   FEET  PER   SECOND   UNDER   ONE  FOOT    HEAD 


46 


Fig.    252. — Characteristic    Curves    of    a    45-Inch    "Samson"    Wheel.     (James 

Leffel  &  Co.) 

greater  range  of  gate  conditions  than  ordinarily  obtained.  Fig. 
252  shows  a  characteristic  curve  of  one  of  the  new  wheels  as  con- 
structed for  this  plant.  The  analysis  was  made  for  the  purpose  of 
•estimating  the  results  which  would  probably  be  secured  under 
service. 

In  Fig.  253  are  shown  the  discharges,  powers,  and  efficiencies 
of  one  unit  of  eight  wheels  under  all  heads  from  8  to  16  feet  at 
full  and  seven-eighths  gate.  Allowances  would  have  to  be  made 
in  order  to  take  into  account  the  difference  between  the  operation 
of  the  eight  wheels  in  the  horizontal  position  connected  in  tandem, 
and  in  the  position  in  which  they  were  tested ;  but  the  diagram 


4I2 


The  Selection  of  the  Turbine. 


shown   gives  an   analysis   from   which   fairly  satisfactory   conclu- 
sions can  be  drawn. 

193.  Graphical  Analysis  as  Proposed  by  Mr.  W.  A.  Waters.— 
A  valuable  method  of  graphical  analysis  is  shown  in  Bulletin  No. 


88 


23C3 


2IC3 


^  1900 


1700 


1500 


1300 


700 


500 


Fig.   253. — Curves  Showing  the  Efficiency  and  the  Maximum   and  Ordinary 
Power  and  Discharge  of  One  Unit  of  8  45-Inch  Samson  Wheels. 

2  of  the  I.  P.  Morris  Company,  in  which  is  discussed  the  variations, 
in  power  and  efficiency  of  a  turbine  wheel  capable  of  giving  13,500 
horse  power  under  a  head  of  65  feet,  and  at  a  speed  of  107  revolu- 
tions per  minute.  This  wheel  was  designed  by  this  Company  for 
the  McCall-Ferry  Power  Company,  and  was  to  work  under  heads 
varying  from  50  to  70  feet. 


Graphical  Analysis  of  W.  A.  Waters. 


414  The  Selection  of  the  Turbine. 

Figs.  254,  255  and  256  and  the  following  description  are  taken, 
with  slight  alterations,  from  the  above  named  Bulletin. 

Curve  No.  I.  Fig.  254,  shows  the  power  which  the  wheel  will 
give  for  heads  varying  from  70  feet  to  zero,  provided  that  the  revo- 
lutions are  allowed  to  vary  as  the  square  root  of  the  head,  and  is 
based  on  equation  (15). 

From  Curve  No.  i,  Fig.  254,  it  will  be  noted  that  at  70  foot  head 
the  wheel  will  develop  15,000  horse  power,  and  from  Curve  No.  6, 
of  the. same  Figure,  it  will  be  noted  that  the  best  speed  of  the 
wheel  under  the  conditions  of  70  foot  head  will  be  in  revolutions 
per  minute.  It  will  also  be  noted  from  Curve  No.  I  that,  under 
50  foot  head,  the  wheel  will  develop  9.150  horse  power,  if  it  be  run 
at  94  revolutions  per  minute.  That  is  to  say,  by  keeping  a  constant 
ratio  between  the  peripheral  speed  of  the  runner  and  the  square 
root  of  the  head  the  efficiency  of  the  wheel  at  varying  heads  is  not 
changed  for  any  given  setting  of  the  gate. 

In  order  to  properly  utilize  the  output  of  the  wheel,  it  is  neces- 
sary that  the  speed  be  kept  constant.  In  order  to  determine  the 
amount  of  power  that  will  be  lost  by  keeping  the  speed  constant 
while  the  head  varies,  the  curves  of  Fig.  255  were  platted  from 
actual  observations. 

Curve  No.  I,  Fig.  254,  is  the  full  gate  readings  of  the  10,500 
horse  power  turbine,  which  was  installed  for  the  Shawinigan  Wa- 
ter and  Power  Company.  This  wheel  was  designed  for  10,500 
horse  power  when  working  under  a  head  of  135  feet,  and  when 
running  at  180  revolutions  per  minute.  The  observations  which 
are  platted  on  this  curve  were  obtained  by  using  the  generator  as 
a  brake  for  the  wheel,  and  a  water  rheostat  was  used  as  a  means  of 
loading  the  generator.  The  speed  was  then  adjusted  to  180  revolu- 
tions per  minute  at  the  wide  open  gate  and  an  observation  made. 
By  varying  the  field  of  the  generator,  the  speed  of  the  unit  was 
varied  without  materially  affecting  the  power  and  without  moving 
the  gate  of  the  wheel.  Observations  were  made  above  and  below 
the  normal  speed  through  as  wide  limits  as  the  rheostat  in  the 
field  circuit  of  the  .generator  would  permit.  The  power  output 
was  determined  by  means  of  accurately  calibrated  electrical  in- 
struments. The  speed  was  determined  by  an  accurately  calibrat- 
ed tachometer.  The  curves  on  this  sheet  give  the  relation  between 
<f>  and  horse  power. 

Referring  back  to  Fig.  254,  and  taking  the  50  foot  head  condi- 
tions, it  should  be  noted  that  for  a  constant  speed  of  107  revolu- 


Graphical  Analysis  of  W.  A.  Waters. 


4*5 


<j)  Horse  Power 


fill/ Gate  CuripYo.  /,  1830® ffi  Ifnif  Shstfririigan 

::%:::        Zv 


Fig.  255.— Curves  of  g>  and  Power  of  Several  I.  P.  Morris  Wheels.     (Repro- 
duced from  Bull.  No.  2  of  I.  P.  Morris.  Co.) 


"^  -.  •»      -V      J   i    -  - 


416  The  Selection  of  the  Turbine. 

tions  per  minute  <j>  would  have  to  increase  from  the  normal  value 
of  about  .68  to  .08.  By  referring  again  to  Fig.  255,  it  will  be 
noted  that  when  <f>  was  0.8,  with  full  gate  opening,  the  power 
.dropped  from  10,650  horse  power  to  10,250  horse  power,  or  about 
3.3  per  cent.  From  this  fact  the  normal  power  as  shown  by  Fig.  i 
may  be  corrected  for  the  new  speed  of  rotation  and  a  point  on 
Curve  No.  2,  Fig.  254  obtained,  giving  the  actual  power  which 
would  be  developed  by  the  wheel  under  the  50  foot  head,  and 
running  at  the  constant  speed  of  107  revolutions  per  minute. 
Curve  No.  2  is  platted  in  this  jnanner  from  Curve  No.  i. 

As  a  check  to  Curve  No.  1,  Fig.  255,  Curves  Nos.  5,  6,  7,  and  8 
have  been  platted,  all  of  which  were  made  from  actual  observa- 
tions, in  the  same  manner  as  Curve  No.  i.  All  of  these  wheels 
are  of  the  Francis  inflow  type,  and  were  designed  for  $-.7,  except 
Curve  No.  6,  which  is  an  outward  flow  Fourneyron  wheel,  and 
was  designed  for  ^=.5.  Curve  No.  5  is  for  a  6,000  horse  power 
wheel  with  gates  in  the  draft  tubes.  The  shape  of  the  curve 
shows  that  the  gate  was  probably  not  entirely  open  when  the  ob- 
servations were  made. 

In  Fig.  256  has  been  platted  efficiency  curves,  which  the  de- 
signed wheel  would  give  under  varying  heads,  and  running  at  a 
constant  number  of  revolutions.  Curve  No.  I  is  an  exact  dupli- 
cate of  the  efficiency  curve  which  was  obtained  on  a  3,500  horse 
power  wheel  working  under  210  foot  head,  and  making  250  revolu- 
tions per  minute.  The  wheel  is  of  the  Francis  inflow  type,  with 
double  runners,  fitted  with  movable  guide  vanes,  similar  to  those 
which  are  proposed  to  be  used  in  the  wheels  for  the  McCall-Ferry 
Power  Company. 

It  will  be  noted  that  the  efficiency  of  the  wheel  reaches  82.3  per 
cent,  at  about  seven-eighths  power,  the  efficiency  dropping  to  Si1/^ 
per  cent,  at  full  gate.  It  will  be  noted  that  the  efficiency  is  very 
high  at  part  load.  This  was  accomplished  in  the  design  of  the  wheel 
by  sacrificing  a  higher  efficiency  at  full  load.  This  curve  has. been 
taken  as  typical  of  the  efficiency  which  would  be  obtained  by  the 
wheel  proposed  for  the  McCall-Ferry  Power  Company,  when  work- 
ing under  a  65  foot  head.  The  efficiency  curve  of  the  10,500  horse 
power  wheel  which  was  supplied  by  the  I.  P.  Morris  Company  to 
the  Shawinigan  Water  and  Power  Company  (See  Fig.  236),  gives 
higher  results  than  the  curve  selected,  but  it  was  thought  that 
Curve  No.  i  is  the  best  for  a  typical  curve. 


Graphical  Analysis  of  W.  A.  Waters.  417 

Curve  No.  i,  Fig.  256  was  platted  by  assuming  that,  at  full  gate, 
3,500  horse  power  corresponded  to  13,500  horse  power  in  the 
wheel  to  be  designed.  The  part  gate  points  of  the  curve  were  ob- 
tained by  proportion.  Curve  No.  3  represents  the  efficiency  and 
power  of  the  wheel  when  working  under  50  foot  head,  and  at  94 
r.  p.  m. 

Point  X  on  this  curve  was  obtained  in  the  following  manner: 
First,  read  on  Curve  No.  1,  Fig.  254  the  power  which  the  wheel 
would  give  under  the  50  foot  head,  and  revolutions  best  suited. 
This  is  found  to  be  9.150  horse  power.  On  Scale  B,  Fig.  256  a 
line  is  drawn  from  9,150  horse  power  to  zero,  forming  Curve  No. 
10.  To  find  what  the  efficiency  would  be  at  8,000  horse  power  un- 
der the  50  foot  head,  take  the  point  at  8,000  horse  power  on  Scale 
B,  projected  horizontally  until  it  intersects  Curve  No.  10,  and 
11,800  horse  power  will  be  read  from  Scale  A.  From  the  effici- 
ency curve  directly  over  8,000  horse  power  on  Scale  A,  the  point,  X, 
will  be  found  on  Curve  No.  3,.  which  gives  the  efficiency  of  the 
wheel  when  developing  8,000  horse  power  under  the  50  foot  head, 
and  running  at  the  revolutions  best  suited,  namely  94. 

This  wheel  is  to  run,  however,  at  107  revolutions  per  mirtute, 
under  all  conditions  of  head,  and  it  is  necessary  to  correct  Curve 
No.  3  for  the  drop  in  power  and  efficiency  due  to  the  increase  in 
speed. 

Referring  to  Curve  No.  I,  Fig.  255,  it  will  be  noted  that  the  pow- 
er varies  when  the  speed  varies,  and  in  the  calculations  of  effi- 
ciency in  Fig.  256,  it  has  been  assumed  that  the  efficiency  varies 
directly  as  the  power.  In  other  words,  it  has  been  assumed  that 
the  quantity  of  water  does  not  vary  when  the  revolutions  are 
changed  with  the  constant  setting  of  the  gate.  This  is  not  strict- 
ly true  but  for  the  observations  as  platted  on  Curve  No.  I,  Fig.  255 
the  quantity  of  water  would  probably  vary  only  one-half  of  one 
per  cent.,  increasing  as  the  revolutions  increase  from  158  to  201. 

Referring  to  Fig.  254,  and  the  50  foot  head,  it  will  be  noted  that 
when  the  speed  is  increased  from  the  best  speed  of  94  revolutions 
to  the  desired  speed  of  107  revolutions,  the  power  falls  3.3  per 
cent,  and  the  power  and  efficiency  of  the  full  gate  point  on  Curve 
No.  3,  Fig.  256  can  be  decreased  3.3  peir  cent,  resulting  in  the  full 
gate  point  on  Curve  No.  2. 

Referring  to  Fig.  255,  Curves  Nos.  I,  2,  3,  and  4,  it  will  be  noted 
that  the  slope  of  these  curves  between  <£  =  0.7  and  <f>  --=0.8  is  about 
the  same,  and,  therefore,  the  power  and  efficiency  of  all  the  points 


The  Selection  of  the  Turbine. 


Fig.  256.— Estimated  Efficiency— Power  Curves  of  the  Proposed  McCall-Ferry 
Wheel.     (Reproduced  from  Bull.  No.  2  of  1.  P.  Morris  Co.) 


Graphical  Analysis  of  W.  A.  Waters.  419 

on  Curve  No.  3,  Fig.  256,  can  be  reduced  by  the  same  percentage, 
namely,  3.3  per  cent.  In  this  manner  Curve  No.  2,  Fig.  256.  is  ob- 
tained, which  gives  the  power  and  efficiency  of  the  wheel  when 
working  under  the  50  foot  head,  and  running  at  the  speed  of  107 
revolutions  per  minute.  In  the  same  manner  Curves  Nos.  5  and  7 
are  platted,  Curves  Nos.  4  and  6  being  deduced  therefrom,  respec- 
tively. In  the  same  manner  Curve  No.  9  is  platted,  and  Curve  No.  8 
deduced  therefrom.  It  will  be  noted  that  Curve  No.  8  lies  on  the 
opposite  side  of  the  parent  curve  to  that  of  the  other  curves. 
Curve  No.  8  crosses  Curve  No.  9  at  13,500  horse  power  on  Scale 
A,  and  beyond  this  point  would  drop  below  Curve  No.  9.  The 
reason  Curve  No.  8  falls  to  the  left  of  Curve  No.  9,  and  shows 
greater  efficiency  at  part  gate  for  the  70  foot  head,  is  because  when 
<j>  changes  from  0.7  to  0.65,  Fig.  255,  the  partial  gate  Curves  Nos.  2, 
3,  and  4,  Fig.  255,  show  the  increase  in  power  and  efficiency. 
These  points,  however,  cannot  be  very  definitely  determined,  but 
it  does  show  that  the  assumption  is  correct  that  the  designed 
wheel,  working  under  the  head  of  70  feet,  and  running  at  107  rev- 
olutions, will  show  higher  percentage  of  efficiency  at  part  gate 
than  when  running  at  the  65  foot  head  and  the  same  powers. 

The  curves  on  Fig.  256  show  that  the  efficiency  is  not  serious- 
ly affected  by  keeping  the  speed  of  the  wheel  constant  under  the 
varying  conditions  of  head.  They  do  show,  however,  that  the 
power  is  seriously  affected  by  keeping  the  speed  of  the  wheel  con- 
stant under  the  varying  conditions  of  head.  The  endings  of  the 
various  curves  show  the  maximum  power,  as  read  on  Scale  A, 
which  the  wheels  will  give  under  that  head. 

These  curves,  therefore,  give  the  performance  of  the  wheel  when 
running  at  a  constant  number  of  revolutions,  and  working  under 
varying  heads  from  50  to  70  feet.  The  curves,  of  course,  are  not 
absolutely  correct.  They  show,  however,  fairly  accurately,  the 
amount  of  variation  in  efficiency  and  power  which  may  be  ex- 
pected from  the  actual  conditions  obtained  with  the  proposed 
wheel  under  the  head  for  which  it  was  designed. 


CHAPTER  XVII 

THE  LOAD  CURVE  AND  LOAD  FACTOR,  AND  THEIR 
INFLUENCE  ON  THE  DESIGN  OF  THE  POWER 
PLANT. 

194.  Variation  in  Load. — All  power  plants  are  subjected  to  more 
or  less  change  in  load,  and  this  continually  changing  load  has  an 
important  bearing  on  the  economy  of  the  plant,  and  should  be  care- 
fully considered  in  its  design  and  construction. 

If  the  power  output  of  any  plant  be  ascertained,  minute  by  min- 
ute or  hour  by  hour,  either  by  means  of  recording  devices  or  by 
reading  the  various  forms  of  power  indicators  usually  provided 
for  such  purposes,  and  a  graphical  record  of  such  readings  be 
made,  a  curve  varying  in  height,  in  proportion  as  the  power  varies 
from  time  to  time,  will  result.  This  curve  is  termed  the  daily 
load  curve.  The  load  curve  itself  will  vary  from  day  to  day  as 
the  various  demands  for  power  vary,  but  it  usually  poss.esses  cer- 
tain characteristic  features  which  depend  on  the  load  tributary  to 
each  plant  and  which  vary  somewhat  as  the  seasons  or  other  con- 
ditions cause  the  load  to  vary. 

The  characteristics  of  the  load  curve,  due  to  certain  demands, 
can  be  quite  safely  predicted.     A  power  plant  in  a  large  city,  for 
example,  will  carry  a  comparatively  small  continuous  night  load. 
This,  in  dark  weather  and  in  winter,  will  be  increased  by  the  early 
risers  who  are  obliged  to  go  early  to  shop   and  factory.     These 
demands  usually  begin  to  affect  the  load  curve  about  5  A.  M.  and 
may  cease  wholly,  or  in  part,  by  7  A.  M.,  depending  on  the  season 
and  latitude.     From  7  to  8  A.  M.  the  motor  load  begins  to  be  felt. 
This  may  reach  a  maximum  from  10  to  12,  and  usually  decreases 
from  12  to  2  during  the  lunch  hours.     The  maximum  load  usually 
comes  in  the  afternoon  when  business  reaches  a  maximum,  and 
when  the  largest  amount  of  power  and  also  light  (in  the  late  aftej;- 
noon)   are  used.     The<  load  begins  to  decrease  after  the  evening 
meal,  as  the  demand  for  light  lessens,  and  may  again  increase  some- 
what as  the  theatres  and  halls  open  for  evenings'  amusements.   The 
character  of  the  load  curves,  due  to  various  loads,  is  best  under- 
stood by  a  study  of  the  actual  curves  themselves. 


Load  Curves  of  Light  and  Power  Plants.  421 

195.  Load  Curves  of  Light  and  Power  Plants. — The  curves 
shown  in  Fig.  257  are  from  the  plants  of  the  Hartford  Electric 
Light  Co.,  of  Hartford,  Conn.,  and  will  illustrate  variation  of  the 
load  curve  at  different  seasons  of  the  year.  These  curves  were 
taken  from  an  article  in  "The  Electrical  World  and  Engineer"  of 
March  8th,  1902.  This  plant  is  a  combined  water  and  steam  pow- 
er plant,  and  is  provided  with  a  storage  battery  to  assist  in  equal- 
izing the  load.  These  curves  are  described  as  follows : 

"On  a  week  day  in  March,  1901,  the  maximum  load  was  1720 
k.  w.  and  the  total  energy  output  was  30249  k.  w.  hours.  The  aver- 
age hourly  load  was  then  1260  k.  w.  or  46  per  cent,  of  the  maximum 
load.  On-  this  same  day  the  battery  discharged  at  the  rate  of  260 
k.  w.  at  the  peak  of  the  load.  In  the  early  morning  hours  of  this  day 
the  load  on  the  system,  apart  from  battery  charging,  reached  its 
minimum  at  612  k.  w.,  or  only  22.5  per  cent,  of  the  maximum  load. 
In  June,  1901,  the  maximum  load  on  a  certain  week  day  was  1390 
k.  w.,  and  the  minimum  250  k.  w.,  or  18  per  cent,  of  the  former. 
The  total  output  on  this  day 'was  2505  k.  w.  hours,  so  that  the 
average  load  during  the  24  hours  was  1046  k.  w.  or  75  per  cent,  af 
the  maximum.  In  January,  the  maximum  load  came  on  between 
4  and  5  P.  M.,  when  lighting  was  the  predominant  factor,  but  in 
July  the  greatest  demand  came  on  the  system  in  the  latter  part 
of  the  forenoon,  and  must  have  been  made  up  in  large  part  by  re- 
quirements for  electric  power.  By  December  1901,  the  maximum 
load  reached  2838  k.  w.  and  the  minimum  612  k.  w.  The  approxi- 
mate capacity  of  all  connected  lamps  and  motors  in  that  month 
was  8530  k.  w.  The  maximum  load  for  the  December  day  of  2838 
k.w.  is  only  33  per  cent,  of  the  connected  capacity.  On  this  day 
the  total  output  was  3219  k.  w.  hours,  so  that  the  average  load 
during  the  24  hours  was  1342  k.  w.  This  average  is  15  per  cent,  of 
the  total  capacity." 

Fig.  258  is  a  combined  annual  load  curve  for  several  years,  and 
not  only  shows  the  increase  in  the  electrical  output  of  this  system 
for  the  years  from  1898  to  1905,  but  also  the  annual  monthly 
change  in  load  from  a  maximum  in  December  or  January  to  a 
minimum  in  June  or  July.  This  variation  fortunately  accompanied 
similar  variation  in  the  flow  of  the  Farmington  River  on  which 
most  of  .the  power  was  developed. 

Up  to  the  middle  of  1898. the  entire  load  of  this  Company  was 
carried  by  a  single  water  power  plant.  The  natural  increase  in 
demand  for  power  necessitated  the  construction  of  a  second  plant 


422 


The  Load  Curve. 
Kilowatts. 


Load  Curves  of  Light  and  Power  Plants. 


4*3 


on  the  same  river,  and  up  to  January  1905,  the  two  water  power 
plants  were  able  to  carry  most  of  the  load,  steam  auxiliaries,  how- 
ever, being  occasionally  used,  as  indicated  by  the  dotted  line. 

Fig.  259  shows  daily  load  curves  from  the  Christiania  Power 
Stations,  of  Christiania,  Norway.  In  this  figure  are  shown  the  max- 
imum, the  minimum,  and  a  mean  curve  for  the  entire  year.  >  The 


1000000 


750000 


500000 


250000 


*H 


Jan.  Jul.  Jan.  Jul.  Jan.  Jul.  Jan.  Jul.  Jan.  Jul.  Jan.  Jul.  Jan.  JuL  Jan.  Jul. 
1898     1899     1900     1901      1902     1908     1904     1905 

Steam 

Water 

Total     

Fig.  258.— Energy  Output  of  Hartford  Electric  Light  Co.     (From 
Electrical  World  and  Engineer. ) 

difference  between  the  maximum  and  minimum  curves  is  here  very 
marked.  This  is  readily  ascribed  to  the  high  latitude  of  Christiania 
as  the  long  twilights  of  summer  render  lighting  at  that  season 
almost  unnecessary,  while  the  very  short  and  dark  days  of  winter 
create  not  only  a  high  maximum  but  a  high  continual  demand  dur- 
ing the  entire  day.  No  data  as  to  kind  of  load  is  available. 

Fig.  260  is  a  power  curve  from  the  New  York  Edison  Company. 

On  August  ist,  1905,  there  were  connected  up  to  the  system  of 
the  New  York  Edison  Company  an  equivalent  of  1,651,917  incan- 
descent lamps,  22,093  arc  lamps,  2,539  k.  w.  in  storage  batteries 


The  Load  Curve. 


and  99,258  H.  P.  in  motors.    The  lighting  load  forms  52.2  per  cent, 
of  the  connected  load. 

The  effect  of  extraordinary  conditions  on  the  load  curve  and  the 
necessity  of  some  kind  of  storage  to  provide  for  the  same,  is  well 
illustrated  by  Fig.  261  which  shows  the  effect  on  the  load  curve 


1000 


A.M. 


4  6 

P.  M. 


Fig.  259. — Typical  Electric  Lighting  Load  Curves.     Christiana,  Norway, 
Power  Stations. 

of  a  lighting  plant  of  a  sudden  thunderstorm.  When  such  a  storm 
occurs  in  the  late  afternoon  the  light  load  from  schools,  offices, 
stores,  etc.,  may  be  suddenly  thrown  on,  and  the  result  may  be  an 
extraordinary  load  which  the  plant  must  meet. 

196.  Factory  Load  Curves. — Shop  and  factory  loads  are  sup- 
posed to  be  the  most  uniform  in  character,  yet  they  are  subject  to 
great  variation,  due  to  the  sudden  turning  on  or  off  of  the  ma- 
chines. Fig.  261  shows  the  load  curve  of  the  Pennsylvania  Rail- 
road Shops  at  Altoona,  Pennsylvania. 

The  shops  of  the  Pennsylvania  Railroad  are  located  in  and  around 
Altoona,  Pennsylvania,  in  groups,  each  group  being  supplied  by  its 
own  power  station.  No  data  as  to  the  number  and  power  of  motors 
connected  up  is  available,  but  the  following  shows  to  some  extent 
how  the  load  is  divided.  The  Machine  Shop  power  plant  embraces 


Factory  Load  Curves. 


425 


2 — 300  k.  w.  generators,  I  Brush  arc  generator  (power  unknown), 
and  a  40  H.  P.  Thompson-Houston  arc  generator  for  lighting  shop 
and  grounds.  At  the  Car  Shops  4-250  k.  w.  and  1-625  k.  w.  gen- 
erators are  used.  Current  is  supplied  to  75  arc  lights  in  shops  and 
yards.  At  the  Junita  shops  3-300  k.  w.  generators  are  used  for 
power  purposes  only.  At  South  Altoona  the  generating  station 


60000 


10         12 
A.  M.  M.  P.  M. 

New  York  Edison  Co.,  Load  Curve,  day  of  Max.  load,  Dec.  22,  1904. 
*  Including  3100  K.  W.  delivered  directly  at  6600  Volts  A.  C. 
Fig.  260.  —Typical  Electric  Lighting  Load  Curve. 

embraces  1-50  k.  w.,  and  2-500  k.  w.,  and  2-300  k.  w.  generators. 
The  loads  are  quite  variable,  as  would  be  expected  in  a  railroad 
shop,  there  being  some  very  heavy  machines  in  intermittent  opera- 
tion, one  planer  running  as  high  as  80  H.  P.,  while  20  H.  P.  motors 
are  numerous.  The  normal  load  is  less  than  the  maximum,  but  the 
latter  is  frequently  reached. 

A,  B  and  C,  Fig.  263,  are  three  typical  factory  lo&d  curves  which 
represent  types  of  load  curves  from  three  different  electric  power 
stations,  A  in  an  Eastern,  B  in  a  Central,  and  C  in  a  far  Western 
state.  These  curves  are  taken  from  an  article  on  "The  Economics 
of  Electric  Power"  in  Cassier's  Magazine  for  March,  1894.  The 
circuits  from  these  stations  are  exclusively  motor  circuits,  the  num- 
ber of  motors  connected  being  given  in  the  following  tables ; 


426 


The  Load  Curve, 


5000 


4000 


3000 


2000 


1000 


A.  M. 


10 


Fig.  261. — Sharp  Thunder  Storm  Peak,  Dickenson  St.  Station,  Manchester, 

Eng. 


A 

B 

C 

Size  of 
Motor 
<H.  P.) 

No.  in 
Use. 

Com- 
bined 
H.  P. 

Size  of 
Motor 
(H.  P.) 

No.  in 
Use. 

Com- 
bined 
H.  P. 

Size  of 
Motor 
(H.  P.) 

No.  in 
Use. 

Com- 
bined 
H.  P. 

i 

3 

H 

I 

3 

I 

i 

4 

1 

31 

31 

2 

I 

* 

•   1 

J 

2 

10 

20 

i 

1 

I 

1 

5 

5 

3 

19 

57 

15 

15 

2 

3 

6 

5 

10 

50 

2 

14 

28 

3 

4 

12 

7* 

3 

22* 

3 

5 

15 

5 

3 

15 

10 

12 

120 

5 

12 

60 

6 

5 

30 

13 

5 

75 

7* 

12 

90 

8* 

3 

25* 

20 

2 

40 

10 

15 

150 

10 

6 

60 

25 

4 

100 

15 

9 

135 

14 

6 

84 

50 

1 

50 

20 

5 

100 

15 

1 

15 

25 

3 

75 

17i 

1 

30 

3 

90 

25 

1 

25 

40 

1 

40 

30 

3 

90 

40 

1 

40 

60 

2 

120 

70 

1 

70 

Total... 

100 

567 

100 

799| 

50 

616* 

Factory  Load  Curves. 


427 


428 


The  Load  Curve. 


7  8  9  10  11  12  1   2  3  4  5  6  7  8   9  10  11  12 


6  7  8  9  10  11  12  1  23   4   5   0   7  8  9  10  11  12 


7 


V 


© 


9  10  11  12  1   2  3  4  5  6  7  8  9  10  11  12 
A.  M.       M.         P.  M. 


Fig.  263.— Typical  Factory  Load  Curves.     (Cassier's  Magazine.) 


Load  Curve  of  London  Hydraulic  Company. 


429 


On  the  circuits  covered  by  the  diagram  B  some  of  the  motors  are 
five  miles  and  more  distant  from  the  power  stations. 

One  deduction  which  may  be  made  from  a  study  of  these  curves 
is  that  in  an  electrical  power  system  where  a  considerable  number 
of  motors  are  employed  the  initial  dynamo  plant  need  not  be  equal 
to  the  total  motor  load.  In  the  case  in  hand  the  curves  show  that 
the  generator  need  be  but  from  25  per  cent,  to  40  per  cent,  of  the 


14000J 


120000 


Fig.   264. — Maximum  Days  of  Pumping. — London  Hydraulic  Supply.     (Cas- 

sier's  Magazine.) 

rated  capacity  of  the  motors  connected.  In  order  to  check  off  this 
phenomenal  condition  actual  meter  readings  were  taken  monthly 
from  fifty-three  different  shops  covering  a  period  of  from  four  to 
six  months,  current  to  these  shops  being  sold  on  the  meter  basis. 
The  results  showed  that  only  25%  per  cent,  of  the  nominal  capacity 
of  the  motors  was  employed,  thus  practically  checking  the  condi- 
tions indicated  by  the  diagrams  of  the  central  power  stations. 

197.  Load  Curve  of  London  Hydraulic  Supply  Company. — Fig. 
264  is  a  load  curve  of  The  London  Hydraulic  Supply  Company, 
which  is  rather  exceptional  in  that  the  power  is  used  almost  en- 
tirely for  running  elevators  and  is  therefore  almost  exclusively  a 
26 


430 


The  Load  Curve. 


Kilowatts 


JUNE  -  89  -1904 


J 


"^ 


BUFFALO 


BATTERIES 


FALLS     POWER     BUFFALO, 


ONAWANOA-LOCKPORT 


FALLS    POWER-TONAWANOA,  LOCKPORT     AND     OLCOTT 

I  .  .  ,  !  ,  I  .  I  |  I  I  |  I  I  I  I  i 


Fig.  L'6\ 


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11000 
10000 
9000 
8000 
7000 
6000 
5000 
4000 
3000 
2000 
1000 

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10 

12 

Fig.  2C6.— Typical  Railway  Load  Curves,  International  Ry.  Co.      (From  Elec- 
trical World  and  Engineer.) 


Railway  Load  Curve.  431 

day  load.  The  London  Hydraulic  Supply  Company  furnishes 
water  under  a  pressure  of  750  pounds  per  square  inch  through  a  sys- 
tem of  mains  86  miles  long.  In  1894,  2915  machines  were  connected 
to  this  system,  of  which  650  were  passenger  elevators,  2000  freight 
elevators  and  cranes,  90  presses  of  various  kinds,  95  motors,  and 
80  fire  hydrants.  Each  1000  gallons  of  water  pumped  represents 
8.738  H.  P.  hours,  therefore,  the  maximum  on  the  diagram  repre- 
sents about  1200  H.  P.  The  preponderant  influence  of  the  elevator 
load  is  shown  in  the  rapid  rise  from  6  to  10  A.  M.  and  the  some- 
what slower  decline  from  4  to  12  P.  M. 

198.  Railway   Load   Curves. — The   power   load   most   subject  to 
violent  fluctations  is  that  utilized  for  railway  purposes.     The  sud- 
den changes  in  the  demand  for  power  occasioned  by  stopping  and 
starting  of  cars,  which  may,  under  some  conditions,  occur  simul- 
taneously are  often  very  rapid  and  the  resulting  load  fluctuations 
very  great. 

Figs.  265  and  266  show  two  sets  of  curves  taken  from  the  power 
charts  of  the  International  Railway  Company  of  Buffalo,  which 
may  be  considered  typical  for  electric  railways.  Each  chart  has 
two  sets  of  curves,  one  for  the  city  lines,  on  which  the  traffic  is 
purely  urban  in  character,  and  the  other  for  the  Tonawanda,  Lock- 
port  and  Olcott  Line,  which  is  an  interurban  line.  In  either  set  the 
total  load  at  any  time  is  represented  by  the  ordinate  to  the  highest 
curve  in  that  set.  The  amount  of  load  carried  by  any  portion  of 
the  system  is  represented  by  the  difference  between  the  ordinates 
to  the  curve  of  that  portion  and  to  the  curve  next  below.  On  the 
urban  lines  two  peaks  will  be  observed,  one  at  8  A.  M.  and  one  at 
6  P.  M.,  for  both  winter  and  summer,  the  afternoon  peak  of  the 
former  being  nearly  75  per  cent  greater  than  the  latter,  however. 
The  load  curve  of  the  interurban  line  appears  to  be  nearly  uniform 
throughout  the  year. 

The  data,  on  page  432,  concerning  these  curves  are  taken  from 
"The  Electrical  World  and  Engineer"  of  December  10,  1904. 

199.  Load    Conditions    for    Maximum    Returns. — It    is    manifest 
that  no  plant  will  receive  its  maximum  returns  without  operating 
at  full  load  all  of  the  time ;  that  if  it  operates  at  less  than  full  load 
its  income  will  be  reduced  unless  more  is  charged  for  power  so 
delivered ;  and  that  if  the  load  carried  for  a  large  portion  of  the 
time  is  comparatively  small  and  the  returns  for  such  power  are  not 
proportionately  large  the  plant  may  be  found  to  be  an  unprofitable 


432 


The  Load  Curve. 


investment.  On  every  plant  the  fixed  charges,  which  include  in 
terest  on  first  cost,  depreciation  charges  and  taxes,  continue  at  a 
uniform  rate  every  hour  of  the  day  and  every  day  of  the  year.  The 
operating  expenses  increase  somewhat  with  the  total  amount  of 
power  furnished  but  not  in  proportion.  An  increase  in  the  total 

Data  from  Curves  of  Figure  265. 


PURCHASED  POWER. 

STORAGE  BATTERIES. 

Grand 
Total. 

Tonawanda. 

Tonawanda. 

Buffalo. 

Lock- 
port. 
Olcott 

Total. 

Buf- 
falo. 

Lock- 
port. 

Total. 

Maximum  H  P  

6,114 
1,667 
4,  636 
111,272 
83,009 

1,985 
319 
1,221 
29,302 
21,859 

8,099 
1,985 
5,857 
140,574 
104,868 

3,752 
79 

1,262 
8,406 
6,271 

635 
40 
274 
3,480 
2,596 

4,387 
119 
1,536 
11,886 
8,867 

12,486 
2,104 
7,393 
152,  460 
113,735 

Minimum  H.  P  

Average  H.  P  

H   P    hours 

K   W     hours 

Maximum  number  of  cars  in  service  in  Buffalo,  408. 
Average  volts  at  D.  C.  busbars,  592. 
State  of  weather:    8  a.  m.,  cloudy;  6  p.  m.,  fair. 
Temperature:    8  a.  m.,  66  degrees  F.;  6  p.  m.,  74  degrees  F. 

Data  from  Curves  of  Figure  26S. 


• 

PURCHASED  POWER. 

STEAM  POWER. 

Grand 
Total. 

Tonawanda. 

Buffalo. 

Lock- 
port. 
Olcott 

Total. 

Niag- 
ara St 

Vir- 
ginia 

St. 

Total. 

Buf- 
falo. 

Maximum  H.  P.  ... 
Minimum  H.  P  
Average  H.  P  

7,622 
2,  303 
6,002 
144,046 
107,458 

2,025 
199 
1,149 

27,584 
20,578 

9,647 
2,502 
7,151 
171,630 
128,036 

3,414 
953 
2,115 
38,442 
28,678 

2,064 
715 
1,641 
4,367 
3,238 

5,478 
1,668 
3,756 
42,809 
31,936 

3,970 
79 
1,224 
7,344 
5,479 

19,  095 
4,249 
12,  131 
221,783 
165,451 

H.  P.,  hours 

K.  W.,  hours.  . 

Average  volts  at  D.  C.  busbars,  592. 

State  of  weather:    8  a.  m.,  cloudy;  6  p.  m.,  cloudy. 

Temperature:    8  a.  m.,  20  degrees  F.;  6  p.  m.  26  degrees  F. 

output  of  a  given  plant,  therefore,  means  a  direct  increase  in  the 
net  earnings  of  the  plant  and  unless  the  power  plant  is  constantly 
operating  at  its  maximum  capacity,  its  earning  efficiency  is  not  at 
the  highest  point. 


The  Load  Curve  in  Relation  to  Machine  Selection.         433 

It  will  be  noted  at  once  that  if  a  machine  can  be  operated  at  its 
full  capacity  for  the  entire  time,  that  the  work  done  will  be  done 
under  the  most  economical  conditions  as  far  as  each  unit  of  output 
(Horse  Power  Hour  or  Kilo-Watt  Hour)  is  concerned.  The  in- 
terest on  the  first  cost  and  other  fixed  charges  will  be  distributed 
among  the  maximum  number  of  power  units.  The  cost  of  wear, 
and  the  repairs,  while  they  increase  with  the  amount  of  power  fur- 
nished, are  not  in  direct  proportion  thereto,  and  decrease  per  unit 
as  the  average  load  carried  reaches  nearer  the  maximum  of  the 
machinery  used.  The  same  is  true  of  the  cost  of  attendance  and 
most  other  operating  expenses. 

200.  The  Load  Curve  in  Relation  to  Machine  Selection. — A  com- 
parison between  the  average  load  carried  and  the  maximum  load 
will  show  the  relation  between  the  machinery  which  it  is  necessary 
to  install  and  the  active,  work  which  it  has  to  do,  and  furnishes  a 
basis  for  the  study  of  the  possible  earnings  of  the  plant. 

The  ratio  between  the  maximum  load  and  the  average  load  is  \ 
called  the  "load  factor."  Some  engineers  use  the  term  "load  factor" 
as  representing  the  ratio  between  the  average  load  actually  carried 
and  the  maximum  capacity  of  the  machinery  operated.  The  writer, 
however,  prefers  the  term  "machine  factor"  to  represent  this  ratio. 
The  same  term  is  also  sometimes  applied  to  the  ratio  of  the  aver- 
age load  to  the  machinery  in  hourly  operation,  but  to  this  the  term 
"hourly  machine  factor"  seems  more  applicable.  The  ratio  of  the 
average  load  to  the  total  capacity  of  the  station  would  seem  best 
represented  by  the  expression  "capacity  factor." 

In  order  to  have  a  plant  work  at  the  maximum  advantage,  it 
must  be  designed  to  fit  the  contingencies  of  the  load.  The  opera- 
tion of  a  machine  at  partial  load  is  not  only  expensive  on  the  basis 
of  fixed  charges,  but  is  still  more  so  on  account  of  the  decreased 
efficiency  under  such  conditions. 

With  a  varying  load,  efficient  operation  usually  involves  the  in- 
stallation of  two  or  more  generators  of  such  capacity  that  a  single 
unit  will  furnish  the  power  required  during  the  hours  of  minimum 
demand  and  at  the  same  time  operate  at  a  fairly  efficient  rate.  As 
the  daily  demand  for  power  increases,  additional  units  are  started 
and  operated,  still  under  economical  conditions,  and  at  the  peak 
of  the  load  one  or  more  additional  units  may  be  cut  in  and  operated 
for  the  limited  time  during  which  the  maximum  demands  prevail. 
Such  an  arrangement  assures  reasonable  economy  of  operation  at 
all  times,  even  when  great  changes  of  load  are  of  daily  occurrence. 


434  The  Load  Curve. 

201.  Influence  of  Management  on  Load  Curve. — The  relations  of 
the  "load  curve,"  the  "load  factor,"  the  "machine  factor"  and  the 
"capacity  factor"  are,  or  may  be,  to  an  extent  controlled  by  the 
business  management  of  any  plant,  and  by  the  selection  and  the 
character  of  the  load  to  be  carried,  where  such  selection  is  possible. 
Each  consumer  of  power  will  develop  a  particular  curve  due  to  the 
character  of  the  work  done,  and  it  is  frequently  possible,  by  a  ju- 
dicious selection  of  customers,  and  especially  by  a  proper  grading 
of  rates,  to  raise  the  load  factor  and  thereby  decrease  the  cost  of 
operation  and  increase  the  net  profits  from  the  plant.     A  study  of 
the  probable  plant  factors  is  necessary  for  the  judicious  selection 
of  machinery  in  order  to  attain  the  most  efficient  operation  and, 
in  a  hydraulic  plant,  in  order  to  properly  design  it  and  conserve 
the  maximum  energy  of  the  stream  that  is  being  developed. 

202.  Relation   of   Load    Curve   to    Stream   Flow   and   Auxiliary 
Power. — Some  of  the  relations  between  the   load   factor  and  the 
conditions  under  which  a  hydraulic  plant  may  have  to  be  operated 
are  shown  by  Figs.  267,  268  and  269. 

In  Fig.  267,  diagram  A  shows  a  typical  daily  load  curve  from  the 
terminal  station  at  St.  Louis,  a  curve  quite  similar  in  general  char- 
acter to  those  previously  shown. 

Diagram  B  shows  the  power  that  must  be  developed  by  a  stream 
in  order  to  take  care  of  the  load  represented  by  this  load  curve, 
under  conditions  where  no  auxiliary  power  or  storage  are  available. 
In  this  case,  it  will  be  noted  that  the  available  water  power  must  be 
equivalent  to  or  greater  than  the  maximum  peak  load,  and  that  all 
power  represented  by  the  area  above  the  load  line,  amounting  in  the 
case  illustrated  to  about  40  per  cent,  of  the  total  available  power, 
will  be  wasted. 

Diagram  C  illustrates  a  condition  where  the  average  load  and 
water  power  are  equal.  In  this  case,  pondage  or  storage,  repre- 
sented by  the  cross-hatched  area  below  the  average  line,  may  be 
utilized  to  furnish  the  peak  power  represented  by  the  cross-hatched 
area  above  the  average  line.  Without  pondage,  the  cross-hatched 
area  below  the  average  load  line  will  represent  the  energy  wasted, 
and  the  cro,ss-hatched  area  above  the  average  load  line  will  repre- 
sent the  energy  which  must  be  supplied  by  auxiliary  power.  With- 
out pondage  the  power  of  the  stream  must  be  utilized  as  it  passes, 
and  in  the  diagram  B,  of  Fig.  267,  the  power  represented  above  the 
load  line  under  such  conditions  must  be  wasted. 


Relation  of   Load  Curve  to  Water  Power. 


435 


sue 


400 


£      300 


;     800 


100 


500 


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RATIOS. 
MINIMUM   TO   AVEBAtC     1  TO   1.7 
MINIMUM    TO    MAXIMUM    1  TO  £.8 
AVERAGE    TO    MAXIMUM  1  TO  1.87 

— 



A.M.                                                                 f    It                                                                  AM. 
8             10            12            e             4             6             8            10           IE              E            4 

— 

TYPICAL    DAILY    LOAD  'CURVE    UNION    TERMINAL    STATION     ST.  LOUIS. 


WATER    POWER    REQUIRED    WITH    10    AUXILIARY    POWER 


STORAGE 


500 


AVERAGE    LOAD    AND    WATER    POWER    EQUAL. 

STORAGE    OR    AUXILIARY    POWER    REQUIRED, 


WATER 

POWER 
UTILIZED. 


POWER 
WASTED. 


FIOM 

STORA8E  . 


AUXILIARY 
POWER. 


RELATION      OF      POWER      SUPPLY      AND     DEMAND 
Fig.  267. 


43$  The  Load  Curve. 

These  same  conditions  are  shown  both  by  diagram  C,  Fig.  268, 
and  diagram  A,  Fig.  269.  In  the  latter,  with  water  power  above 
the  average  load  of  the  plant,  the  peak  load  must  be  supplied  by 
auxiliary  power,  although  more  water  power  than  would  be  suffi- 
cient to  handle  it  is  daily  wasted. 

Diagram  B,  Fig.  268,  shows  a  condition  with  low  water  power 
no  storage  available,  and  the  power  less  than  the  average  load.  In 
this  case  the  water  power  wasted  is  comparatively  small,  and  the 
amount,  and  especially  the  capacity,  of  the  auxiliary  power  be- 
comes large. 

Diagram  C,  Fig.  268,  represents  a  water  power  condition,  where 
the  power  available  is  less  than  the  average  load,  where  storage 
is  practically  unlimited,  and  some  auxiliary  power  is  necessary  in 
order  to  carry  the  peak  of  the  load.  Under  these  conditions,  the 
water  power,  which  would  otherwise  be  wasted  during  the  time 
of  minimum  load,  is  impounded,  and  can  be  utilized  together  with 
the  auxiliary  power  at  times  of  maximum  load.  The  diagram 
shows  a  method  of  utilizing  the  minimum  capacity  of  auxiliary 
power  by  utilizing  the  stored  water  power  to  its  greatest  advan- 
tage, and  utilizing  auxiliary  power  uniformly  throughout  the 
period  where  auxiliary  power  is  demanded. 

Diagram  A,  Fig.  269,  represents  the  same  conditions  where  stor- 
age is  limited,  and  auxiliary  power  is  necessarily  required  to  help 
out  the  peak  load  conditions.  In  this  case  only  a  certain  amount 
of  the  spare  water  can  be  stored,  the  balance  being  wasted  at  times 
where  it  cannot  be  continuously  utilized. 

The  conditions  for  reducing  the  total  amount  of  auxiliary  power 
by  utilizing  the  storage  to  advantage  is  shown  in  the  same  manner 
as  in  diagram  C,  Fig.  268. 

Diagram  B,  Fig.  269,  shows  a  method  of  utilizing  the  minimum 
capacity  of  auxiliary  power  in  a  plant  where  the  water  power  is 
below  the  average  load  and  the  pondage  is  practically  unlimited. 
This  is  accomplished  by  the  continuous  operation  of  the  auxiliary 
plant  and  the  storage  of  water  power  during  the  hours  of  low  con- 
sumption, for  utilization  during  the  hours  of  peak  load. 

A  careful  and  detailed  study  of  the  load  curve  and  load  factor; 
the  method  of  increasing  the  latter  and  of  designing  the  most 
economical  plant  to  take  care  of  the  condition  to  be  met;  and  the 
adjustment  of  rates  to  attain  equitable  returns  to  the  investor  at 
reasonable  price  to  the  consumer,  are  matters  of  plant  design 
worthy  of  the  best  efforts  of  the  engineer. 


Relation  of  Load  Curve  to  Water  Power. 


437 


5CU 


400 


300  -i 


~    aoo 


100 


SOD 


AUXILIARY    POWER    REQUIRED  .   NO    STORAGE    AVAILABLE 
WATER    POWER   GREATER    THAN  AVERAGE    LOAD  . 


AUXILIARY    POWER    REQUIRED.  NO   STORAGE    AVAILABLE 
WATER    POWER   LE88   THAN  AVERAGE   LOAD  . 


500 


AUXILIARY    POWER    REQUIRED  .  STORAGE    UNLIMITED 
WATER    POWER    LESS    THAN  AVERAGE    LOAD 


WATER 
PfiWER 
UTILIZER. 


POWER 
WASTED 


FROM 
ITO«A(E 


AUXILIARY 
POWER 


RELATION     OF     POWER     SUPPLY      AND     DEMAND    . 

Fig.  268. 


433 


The  Load  Curve. 


AUXILIARY    POWER    REQUIRED      STORAGE    LIMITED 
WATER    POWER    GREATER    THAN  AVERAGE    LOAD 


500 


400 


I  ""===:? 


r:     Z-00 


100  - 


AUXILIARY   POWER   [MINIMUM    REQUIRED]    IN    CONTINUOUS    SERVICE 
STORAGE    UNLIMITED 

WATER 

r\KKXiPowru  .*,  x 

STORAGE 


POWtB 
UTILIZED  < 


POWER 
WASTED 


POWER 
FROM 

STORAGE 


AUXILIARY 
POWER 


RELATION     OF     POWER     SUPPLY      AND     DEMAND 

Fig.  269. 


Literature  on  Load  Curve.  439 

LITERATURE. 
REFERENCES  OF  LOAD  CURVES  AND  LOAD  FACTORS. 

1.  Load  Curves  of  Electric  Central  Station.    Elektrotechnische  Zeitschrift 

Vol.  25,  page  G8.     Jan.  28,  1904. 

2.  Influence  of  Load  Factor  on  the  Cost  of  Electrical  Energy.     Edmund  I*, 

Hill.     Electrician  (Lon.).     Feb.  10,  1905. 

3.  Load  Factor — Its  Effect  upon  an  Electricity  Station.    Alex  Sinclair.    Elec 

trician,  London,  June  30,  1905. 

4.  Distribution  of  Power  Load  of  Electricity  Works.     Electrician    (Lon.), 

July  28,  1905. 

5.  The    Load    Factor    of    Electric    Generating    Stations.     Norberg^Schultz, 

Coustiania.    Elektrotechnische  Zeitschrift.    Vol.  26,  p.  919,  Oct. 
5,  1905. 

6.  The  Effect  of  Load  Factor  on  Cost  of  Power.     E.  M.  Archibald.    Eng. 

News,  Vol.  53,  p.  169.     Feb.  16,  1905.     Elec.  Age,  Nov.  1906. 

7.  Electrical  Transmission  of  Water  Power.     Alton  D.  Adams.     Chap.  I  and 

II.     New  York.     McGraw  Pub.  Co.     1906. 

8.  Economy   of  Continued   Railway -and   Lighting  Plants.     Ernest   Ganzen- 

bach.     St.   Ry.  Review,  Feb.  15,   1906.     Elec.  World  and  Engr. 
Jan.  27,  1906. 

9.  Central  Station  Power.     E.  P.  Espenschied,  Jr.    Proc.  Engrs.  Soc.  Wes. 

Penn.    Mar.  1906. 

10.  Relation  of  Load,  Factor  to  the  Evolution  of  Hydro-Electric  Plants.     S.  B. 

Storer.     Am.  Inst.  Elec.  Engrs.     Mar. -23,  1906. 

11.  Notes  on  Design  of  Hydro-Electric  Stations   (With  Reference  to  the  In- 

fluence of  Load  Factor).     David  D.  Rushmore.     Proc.  Am.  Inst. 
Elec.  Engrs.     April,  1906. 

12.  Effect  of  Day  Load  on  Central  Station  Economy.     J.  P.  Janes.     Elec.  Re- 

view, N.  Y.     May  12,  1906.. 

13.  Sale  and  Measurement  of  Electric  Power.     S.  B.  Storer.     Electrical  Age, 

Aug.  1906. 

14.  Sale  of  Water  Power  from  the  Power  Company's  Point  of  View.     C.  E. 

Parsons.     Eng.  Record,  Aug.  11,  1906. 

15.  Contracting  for  Use  of  Hydro-Electric  Power  on  Railway  Systems.     G.  A. 

Harvey.     Elec.  Age,  Sept.  1906. 

1C.  The  Sale  of  Electric  Power.     Eng.  Record,  Nov.  3,  1906. 
17.  Flat  Rates  for  Small  Water  Power  Plants.    J.  S.  Codman.    Elec.  Wld, 

and  Engr.,  Nov.  3,  1906. 


CHAPTER  XVIII. 


THE  SPEED  REGULATION  OF  TURBINE  WATER 
WHEELS. 

203.  The  Relation  of  Resistance  and  Speed. — The  power  delivered 
by  any  water  wheel  may  be  expressed,  in  terms  of  resistance  over- 
come by  the  wheel  through  a  known  distance  and  in  a  known  time 
by  the  formula  (See  equation  i,  Section  177,  Chap.  XVI). 

2x1  w  n 


(1) 


P  = 


33000 


The  second  term  of  this  equation  may  be  divided  into  two  fac- 
tors :  first, 

2x1  w 

33000 

which  may  be  called  the  resistance  factor  and  which  is  the  resist- 
ance overcome  or  power  produced  by  the  wheel  per  revolution  per 


.UTlONS    PCP     HINUTC 

Fig.  270. 


minute ;  and  n,  the  number  of  revolutions  per  minute.  The  product 
is  the  horse  power  of  the  wheel. 

^  In  any  wheel  operating  with  a  fixed  gate  opening  and  under  a 
fixed  head  the  speed,  n,  will  always  increase  as  the  resistance,  w, 
decreases,  and  will  decrease  as  the  resistance  increases. 


Self  Regulation  with  Variable  Speed  and  Resistance.      441 

In  Fig.  270  the  line  AB  shows  the  relation  of  speed  to  resist- 
ance in  a  turbine  operated  with  a  single  fixed  gate  opening  and 
for  the  full  range  of  load  conditions  (as  determined  by  experiment) 
from  A,  at  which  the  resistance,  w,  was  so*  great  as  to  hold  the 
motor  stationary,  to  B  where  the  resistance  was  completely  re- 
moved and  the  entire  energy  of  the  applied  water  was  expended 
in  overcoming  the  friction  of  the  wheel,  or  rejected  as  velocity  en- 


HEAD    WATER 


Fig.  271. 


ergy  in  the  water  discharged  therefrom.  From  this  figure  it  is 
evident  that  if,  at  any  fixed  gate  opening,  a  wheel  'is  revolving  at 
a  given  speed,  n,  and  the  resistance,  w,  is  decreased  to  w"  the  speed 
will  increase  to  n",  while  if  the  resistance  increases  to  w'  the  speed 
will  decrease  to  n'. 

204.  Self-Regulation  in  a  Plant  with  Variable  Speed  and  Resist- 
ance.— At  Connorsville,  Indiana,  is  a  pumping  plant  (Fig.  271)  in 
which  a  horizontal  shaft  turbine  is  directly  connected  through 
friction  clutches  to  two  rotary  pumps.  For  operation  the  turbine 
gates  are  opened  until  the  pump,  or  pumps,  speeding  up  to  a  suit- 
able r.  p.  m.,  produces  the  desired  pressure  in  the  distributing  sys- 


442       The  Speed  Regulation  of  Turbine  Water  Wheels. 

tem.  The  work  of  the  pump  under  these  conditions  in  pumping 
water  at  the  speed  of  operation  against  the  desired  pressure  equals 
the  work  done  by  the  quantity  of  water  q  passing  through  the  tur- 
bine, less  friction  and  other  losses.  If  the  pressure  falls,  the  loads 
become  unbalanced:  i.  e.,  the  resistance  is  reduced  and  the  tur- 
bine and  pump  increase  in  speed  until  the  balance  is  restored.  If 
the  pressure  rises  the  machine  slows  down  until  there  is  again 
a  restoration  of  balance  between  the  power  of  the  turbine,  the 
purnp  load  and  friction  losses. 


IONS  pen  MINUTE 

Fig.  272. 

To  pump  water  against  an  increased  pressure,  it  is  necessary  to 
increase  the  gate  opening  of  the  turbine.  In  its  regular  daily  work 
the  varying  demand  for  water  is  thus  supplied  by  the  self-regula- 
tion of  the  two  machines  used  and  no  governor  is  needed.  The 
conditions  of  operation  are  similar  to  those  illustrated  in  Fig. 
270. 

205.  The  Relations  Necessary  for  Constant  Speed. — Fig.  272 
is  a  diagram  drawn  from  experimental  or  test  observations  and 
similar  to  Fig.  270  except  that  the  relations  between  speed  and  de- 
sistance  are  shown  for  various  gate  openings. 

It  is  evident  that  if  the  wheel  must  operate  at  a  fixed  speed,  n,  and 
the  resistance,  w,  increases  to  w'  or  decreases  to  w",  it  will  be  neces- 
sary to  increase  the  gate  opening  from  %  gate  to  full  gate  in  the 
first  case  and  to  decrease  it  to  %  gate  in  the  second  case  in  order  to' 
maintain  the  speed  uniform. 


The  Ideal  Governor.  443 

An  examination  of  the  load  curves  described  in  Chapter  XVII 
shows  that  changes  in  load  are  constantly  in  progress.  For  the 
satisfactory  operation  of  water  wheels,  under  these  constant  and 
irregular  changes  in  load,  automatic  regulation  of  the  turbine  gates 
becomes  necessary-  This  is  accomplished  through  the  water  wheel 
governor  which  regulates  the  gates  through  the  various  classes  of  ' 
gate  mechanisms  described  in  Chap.  XIII. 

206.  The  Ideal  Governor.  —  The  power  output  of  a  water  tur- 
bine in  terms  of  energy  applied  to  the  wheel  is  expressed  by  the 
formula.  • 


(2) 


q    =  cu.  ft.  per  second  of  water  used  by  the  wheel. 
H'  =  net  available  head. 
E   =  efficiency  of  the  wheel. 
P   =  horse  power  developed. 

Any  sudden  increase  or  decrease  of  load,  w,  will  produce  a  cor- 
responding decrease  or  increa'se,  respectively,  in  the  speed,  n,  of 
the  machine  as  shown  by  Fig.  270  unless  the  energy  applied  to  the 
turbine  is  immediately  changed  to  correspond.  The  ideal  turbine 
governor  would  effect  a  change  in  output  by  varying  only  q,  thus 
obtaining  perfect  water  economy  by  conservmg^ttnneeded  water 
for  future  use.  This  is  not  possible  in  practice  as  head,  water,  and 
therefore  efficiency  are  usually  wasted  when  operating  a  wheel  un- 
der other  than  its  normal  load  and  during  the  change  in  load. 

207.  Present  Status,  —  The  success  of  the  comparatively  recent 
application  of  hydraulic  power  to  the  operation  of  alternators  in 
parallel  and  to  the  generation  of  current  for  electric  lighting  street 
railway  and  synchronous  motor  loads  has  been  largely  dependent 
upon  the  possibility  of  obtaining  close  speed  regulation  of  the  gen- 
erating units  accompanied  with  good  water  economy  and  without 
undue  shock  upon  machinery  and  penstocks  while  working  under 
extremely  variable  loads. 

The  degree  of  success  thus  far  obtained  in  the  development 
(necessitated  by  the  above  conditions)  of  automatic  turbine  gov- 
ernors, although  achieved  from  the  experimental  standpoint  almost 
exclusively,  has  been  remarkable.  Instances  are  now  by  no  means 
uncommon  where  hydro-electric  units  working  upon  variable  loads 
are  controlled  as  ,  satisfactorily  as  modern  steam  driven  units.  To 
accomplish  this  result  the  conditions  must  be  especially  favorable. 


444       The  Speed  Regulation  of  Turbine  Water  Wheels. 

Success  in  this  feature  of  hydro-electric  design  is  by  no  means 
uniform,  however,  and  the  fre.quent  failure  to  realize  satisfactory 
results  can  often  be  ascribed  to  the  lack  of  proper  consideration  of 
the  arrangement  of  the  mechanical,  hydraulic,  and  electrical  ele- 
ments of  the  plant,  wheels,  and  generators,  rather  than  to  any  in- 
herent defects  in  the  governor  itself.  The  power  plant,  the  tur- 
bines, the  generators,  and  the  governors  are  commonly  designed  by 
four  different  parties  without  proper  correlation  of  study  and  de- 
sign. At  present  neither  experimental  data  nor  theoretical  formula 
are  available  by  which  the  hydro-electric  engineer  can  design  hi? 
plant  for  an  assumed  speed  regulation,  or  can  predetermine  the 
speed  regulation  which  is  possible  with  a  given  installation  or  the 


120  140 

PERCENT  OF  NC3MAL  CANDLE  PCWER 


i60 


130 


Fig.  273. 


time  required  for  the  return  to  normal  speed, — and  yet  the  gov- 
ernor builder  is.  commonly  required  by  the  engineer  to  guarantee 
these  operating  results.  The  predetermination  oif  speed  variations 
'during  portions  of  the  steam  cycle  and  at  load  changes  has  received 
careful  study  in  the  design  of  reciprocating  steam  engines  and  the 
desirable  per  cent  of  speed  regulation  is  freely  guaranteed  and 
readily  obtained  through  careful  study  and  analysis  by  the  designer. 
The  same  amount  of  study  is  warranted  but  seldom  or  never  given 
to  the  problem  of  speed  regulation  in  water  power  work. 

208.  Value  of  Uniform  Speed. — Uniform,  or  nearly  uniform, 
speed  is  of  great  economic  value  in  the  operation  of  a  plant  but  adds 
to  the  first  cost  and  may  also  result  in  a  waste  of  water.  The  cor- 
rect solution  of  any  given  problem  of  speed  regulation  involves  a 
compromise  between  first  cost,  water  economy  and  speed  regula- 
tion. 

A  pecuniary  value  cannot  well  be  placed  upon  good  speed  regu- 
lation. It  differs  from  poor  speed  regulation  chiefly  in  procuring  a 
more  satisfactory  operation  of  motor  driven  machinery  and  in  pro- 
ducing a  more  constant  incandescent  light.  Fluctuations  in  the 
brightness  of  a  light  are  annoying,  and  tend  to  create  dissatisfac- 
tion among  consumers.  Fig.  273  shows  the  general  way  in  which 


The  Problem. 


445 


the  candle  power  of  an  incandescent  light  varies  with  the  impressed 
voltage.*  A  pressure  variation  of  5  per  cent.,  and  hence  also  a 
speed  variation  of  a  similar  amount,  is  shown  to  produce  a  much 
larger  variation  in  candle  power  of  the  light, — in  this  case  about 
25  to  30  per  cent. 

209.  The  Problem. — Where  (as  in  Fig.  271)  a  turbine  is  operating 
under  balanced  conditions  and  the  resistance  changes  in  magni- 
tude, the  turbine  does  not  at  once  assume  the  new  speed  relations 
corresponding  to  the  change  in  resistance.  The  inertia  of  the  mov- 
ing parts  of  the  wheel  and  of  the  column  of  water  in  the  penstock, 


Fig.  274. 


Fig.  275. 


turbine  and  draft  tube,  tends  to  maintain  uniformity  of  speed,  and 
the  wheel  gradually  changes  in  speed  to  that  corresponding  to  the 
new  conditions.  In  such  cases  the  speed  of  operation  is  not  essen- 
tial and  the  delay  in  reaching  the  speed  corresponding  to  the  re- 
sistance or  work  the  turbine  must  perform  is  usually  unimportant. 

When,  as  in  Fig.  272,  the  wheel  is  designated  to  operate  at  a 
fixed  speed,  the  uniformity  of  speed  becomes  a  matter  of  greater 
or  less  importance  depending  on  the  character  of  the  work  the  wheel 
is  to  perform.  In  this  case  the  inertia  of  the  wheel  and  of  all  rotat- 
ing parts  of  other  machinery  connected  thereto  tends  to  maintain 
a  constant  speed.  On  the  other  hand,  the  flow  of  water  in  penstock, 
turbine,  and  draft  tube  must  ,be  changed  in  quantity,  (Eq.  2), 
hence  in  velocity,  and  its  inertia  therefore  tends  to  produce  a  change 
in  head  and  to  produce  effects  opposite  to  those  desired  for  efficient 
regulation. 

The  conditions  of  installation  have  a  marked  effect  on  the  diffi- 
culties of  turbine  governing.  If  (as  in  Fig.  274)  the  turbine  is  in- 
stalled in  an  open  pit  and  has  only  a  short  draft  tube,  and  the  water 

*  See  American  Electrician,  Vol.  XIII,  No.  7.     July,  1901,  by  F.  W.  Wilcox. 

27 


446       The  Speed  Regulation  of  Turbine  Water   Wheels. 

flows  to  the  gates  from  every  direction,  the  velocity  of  flow  from 
all  directions  is  very  low.  The  quantity  of  water  which  moves  at  a 
high  velocity  in  confined  to  that  in  the  wheel  and  draft  tube  and 
the  change  in  the  velocity  and  momentum,  due  to  a  change  in  the 
gates,  produces  no  serious  effects.  If,  however,  water  be  con- 
ducted to  and^from  the  wheel  through  a  long  penstock  and  draft 
tube  (as  illustrated  by  Fig.  275)  the  conditions  become  quite  differ- 
ent. In  this  case  a  large  amount  of.  energy  is  stored  in  the  moving 
column  of  water  and  a  change  in  its  velocity  involves  a  change  in 
its  kinetic  energy  which  may,  if  an  attempt  is  made  at  too  rapid  reg- 
ulation, leave  the  wheel  deficient  in  energy  when  increased  power  is 
desired,  or,  when  the  power  is  decreased,  may  produce  such  shocks 
as  will  seriously  affect  regulation  or  perhaps  result  in  .serious  in  jun- 
to the  penstock  and  wheel. 

210.  Energy  Required  to  Change  the  Penstock  Velocity. — An 
increase  or  decrease  of  load  requires  an  ultimate  increase  or  de- 
crease in  velocity  of  the  water  in  the  penstock.  Work  has  to  be 
done  upon  the  water  to  accelerate  it  and  must  be  absorbed  in  order 
to  retard  it.  The  total  available  power  which  can  be  expended  for 
all  purposes  at  any  instant  during  the  acceleration  is  (since  vH  is 
proportional  to  qH)' proportional  to  the  product  of  the  instantane- 
ous velocity  and  the  supply  head.  This  total  power  is  thus  defi- 
nitely limited  and,  hence,  the  work  required  to  accelerate  the  water 
must  be  obtained  at  the  expense  of  the  work  done  upon  the  wheel. 

Thus,  when  an  increase  of  load  occurs  the  gate  is  opened  by  the 
governor,  and  the  immediate  result  is  a  decrease  in  the  power  out- 
put of  the  wheel,  even  below  its  original  value,  and  is  diametrically 
opposed  to  the  result  desired.  This  counter  effect  may  last  for  sev- 
eral seconds,  and,  unless  sufficient  reserve  energy  in  some  form 
is  available  to  partially  supply  this  deficiency,  the  speed  of  the 
wheel  may  fall  considerably  before  readjustment  to  normal  power 
can  take  place. 

In  the  same  way  an  excess  of  energy  must  be  absorbed  to  de- 
crease the  velocity  at  time  of  decreasing  load.  This  may  be  ex- 
pended upon  the  wheel  thus  increasing  the  speed  above  normal,  or 
it  may  be  dissipated  in  one  of  several  ways  to  be  discussed  later. 

The  water  in  the  draft  tube  must  be  accelerated  and  retarded  at 
each  change  of  gate  opening  and  its  kinetic  energy  changed  at  the 
expense  of  the  power  output  in  exactly  the  same  manner  as  that  in 
the  penstock.  For  this  reason  it  should  be  included  in  all  calcula- 
tions as  a  part  of  the  penstock.  One  additional  precaution  must  be 


Hunting  or  Racing.  447 

taken :  if  the  draft  head  is  large  a  quick  closure  of  the  turbine  gate 
may  cause  the  water  in  the  draft  tube  to  run  away  from  the  wheel 
(actually  creating  a  vacuum  in  the  draft  tube)  and  then  return 
again  causing  a  destructive  blow  against  the  wheel. 

211.  Hunting  or  Racing. — The  regulation  of  both  steam  engines 
and  hydraulic  turbines  as  now  accomplished  is  one  of  degree  only 
since  a  departure  froim  normal  speed  is  necessary  before  the  gov- 
ernor can  act.    Since  the  immediate  effect  of  the  gate  motion  is  op- 
posite to  that  intended,  the  speed  will  depart  still  further  from  the 
normal.     This  tends  to  cause  the  .governor  to  move  the  gate  too 
far  with  the  result  that  the  speed  will  not  only  return  to  normal 
as  soon  as  the  inertia  of  the  water  and  of  the  rotating  parts  is  over- 
come, but  may  rush  far  beyond  normal  in  the  opposite  direction. 
The  obvious  tendency  is  thus  to  cause  the  speed  to  oscillate  above 
and  below  normal  to  the  almost  complete  destruction  of  speed  reg- 
ulation. 

A  successful  governor  must  therefore  "anticipate"  the  effect  of 
any  gate  movement.  It  must  move  the  gate  to,  or  only  slightly  be- 
yond, the  position  which  will  give  normal  speed  when  readjust- 
ment to  uniform  flow  in  the  penstock  has  taken  place.  A  governor 
with  this  property  or  quality  is  commonly  said  to  be  "dead-beat." 
In  Chap.  XX  several  expedients  are  shown  for  the  automatic  elim- 
ination of  excessive  racing. 

212.  Nomenclature. — The  following  symbols  will  be  used  in  the 
mathematical  discussions  which  follow : 

A  =  cross-sectional  area  of  penstock  in  sq.  ft. 

R          V  +  V° 
~-^=^ 

c  =  friction  coefficient  for  flow  in  pipe  lines  =  — —  (1  -f-  f  -^  4-  etc.) 

Da  =  maximum  rise  of  water  in  standpipe  above  the  forebay  when  full 

load  (v  =  Vf)  is  rejected  by  the  wheels. 

D'  =  drop  of  water  in  standpipe  below  original  friction  gradient  all  in- 
fluences considered. 

D  ='  ditto,  friction  in  penstock  neglected. 
Db  =  drop  of  level  in  standpipe  below  forebay. 
d  =  diameter  of  penstock  (closed  circular)  in  feet, 
e  —  2.71828  =  base  of  natural  system  of  logarithms. 
F  =  cross-sectional  area  of  the  standpipe  in  square  feet, 
f  —  "friction  factor"  in  penstock, 
g  =  acceleration  due  to  gravity  in  feet  per  second. 
H  —  total  available  power  head  in  feet. 

H'  =  effective  head  at  the  wheel  =  H  —  h  for  any  given  uniform  velocity, 
V,  in  the  penstock. 


448       The  Speed  Regulation  of  Turbine  Water  Wheels. 

h  =  instantaneous  effective  head  at  the  wheel  during  changes  of  velocity 

in  the  penstock, 
hg  =  head  which  is  effective  at  any  instant  in  accelerating  the  water  in 

the  penstock  and  draft  tube. 
hF  =  friction  loss  in  penstock  for  normal  flow  with  a  given  head  and  gate 

opening, 
hf  =  variable  head  lost  by  friction  entrance,  etc.,  in  penstock  when  the 

velocity  is  v. 
I  =  moment  of  inertia  or  fly  wheel  effect  of  revolving  parts  in  pounds  at 

one  ft.  radius  =  ft.8  Ibs. 
K  =  energy  delivered  to  the  wheel. 

A  K  =  excess  or  deficient  energy  delivered  to  wheel  during  change  of  load. 
A,  Ki  =  excess  of  deficient  energy  delivered  to  wheel  due  to  excess  or  defic- 
iency in  quantity  of  water  during  load  change. 
A  £2=  ditto,— due  to  energy  required  to  accelerate  or  retard  the  water  in 

the  penstock . 
A  Ka  —  ditto, — due  to  sluggishness  of  gate  movement. 

K'  =  kinetic  energy  in  foot  pounds  of  revolving  parts  at  speed  S. 
A  K'  —  increment  (+  or  — )  in  K'  due  to  load  change. 


2.31V 
1  1=  length  of  penstock  in  feet. 

M  =  slope  of  the  v-t  curve  when  v  =  — ^-~ (equation  19). 

Po  =  initial  horse  power  output  from  the  water  wheel. 

pi  =  the  horse  power  output  from  the  water  wheel  corresponding  to  the 

new  load. 
Q  =  discharge  of  the  wheel  under  normal  effective  head  H'  for  any  given 

load, 
q  =  instantaneous  discharge  of  wheel  in  cubic  feet  per  second  during  load 

change. 

R  =  ratio  of  actual  deficient  or  excess  work  done  on  wheel  to  that  com- 
puted. 

S  =  normal  r.  p.  m.  of  the  wheel  and  other  rotating  parts. 
A  S  —  S  —  Si  =  temporary  change  in  speed. 
Si  =  speed  in  revolutions  per  minute  after  load  change. 
T'  =  approximate  time  required  lor  acceleration  or  retarding  of  water 

from  velocity  v0  to  vi. 
T"  =  the  time  required  for  the  governor  to  adjust  the  gate  after  a  change 

of  load. 

t  =  variable  time  after  gate  movement. 
V  -  normal  (and  hence  maximum  possible)  velocity  in  the  penstock  with 

given  head  and  gate  opening, 
v  =  instantaneous  variable  velocity  in  the  penstock  while  adjusting  to  a 

new  value. 

v0  =  velocity  in  penstock  at  the  instant  of  gate  change. 
Vj  =  velocity  in  the  penstock  required  for  new  load. 


Water  Hammer. 


449 


w  =  weight  of  a  cubic  unit  of  water  in  Ibs. 

Y  =  maximum  departure  of  head,  h,  from  normal  with  use  of  stand- 
pipe, — discharge  of  wheel  assumed  constant  at  the  abnormal  head 
(see  Da  and  Db). 

y  =  variation  of  water  level  in  the  standpipe  from  forebay  level  =  H  —  h. 

d  =  speed  regulation  or  per  cent  variation  of  speed  from  normal. 

213.  Shock  or  Water  Hammer  Due  to  Sudden  Changes  in  Ve- 
locity.— The  acceleration  or  retardation  of  a  moving  body  requires 
an  unbalanced  force.  Since  acceleration  and  retardation  are  iden- 


Fig.  276. 


tical,  except  as  to  sign,  the  required  accelerating  force  may  in  all 
cases  be  expressed  as  follows : 

Force  =  mass  X  acceleration. 

Acceleration,   or  the   rate  at  which   the   velocity  increment  in- 
creases per  increment  of  time,  is  expressed  by  the  formula : 

dv 
(3)  Acceleration  —  — r— 

The  mass  of  water  to  be  accelerated  is 


(4) 


Mass  — 


Alw 


Figs.  276  and  277  show  the  conditions  existing  during  an  in- 
crease and  decrease  of  velocity  respectively.  If  the  draft  tube  were 
closed  at  the  lower  end  and  no  water  leaving,  there  would  be  a 
total  force,  equal  to  the  hydraulic  pressure  over  the  area  of  the 
penstock,  or  wAH,  tending  to  move  the  water. 


450       The  Speed  Regulation  of  Turbine  Water  Wheels. 


If  the  water  is  flowing  with  a  velocity  v  the  turbine  offers  a  re- 
sistance to  flow  represented  by  the  effective  head,  h,  at  the  wheel, 
and  the  penstock  offers  a  resisting  head  hF  composed  of  friction,  en- 
trance, and  other  losses.  If  the  velocity  remains  uniform,  h=H', 
and  the  forces  are  balanced  thus: 

(5)  H  =  H'  +  hP 

If  the  opening  of  the  turbine  gate  is  now  suddenly  increased,  the 
head  H'  at  the  wheel,  will  fall  to  the  value,  h,  (shown  in  Fig.  276) 
which  is  required  to  force  the  given  amount  of  water,  Av,  through 


Fig.  277. 


the  wheel.  On  the  other  hand,  if  the  gate  opening  is  decreased  the 
pressure  head  must  rise  above  H'  (as  shown  in  Fig.  277)  in  order 
to  discharge  the  water  through  the  wheel.  This  change  ha  in  the 
head  H'  disturbs  the  equilibrium  of  forces  shown  by  equation 
(5)  making 

(6)  ha  =  H  —  h  —  hf 

Only  the  head  ha  is  effective  in  accelerating  or  retarding  the 
water  and  the  force  resulting  from  this  head  is  wAha.  Substitut- 
ing this  value  and  those  of  equations  (3)  and  (4)  in  equation  (2) 
we  obtain: 


Alw      dv 


dt 


or 


(7) 


dv 


of  velocity  change) 


Permissible  Rate  of  Gate  Movement.  451 

The  value  of  ha  given  by  formula  (7)  is  a  general  expression  for 
the  change  in  pressure-head  due  to  a  change  of  velocity  or  for  the 
head  which  must  be  impressed  to  produce  a  desired  change  in 
velocity.  When  in  excess  of  the  static  pressure  as  shown  in  Fig. 
277,  it  is  commonly  called  "water  hammer."  (See  Appendix  A.) 

If  the  closure  of  the  gates  is  rapid  the  value  of  ha  is  large  and 
the  column  of  water  is  set  into  vibration  or  oscillation.  If  the 
partial  closure  of  gate  is  sufficiently  slow  to  allow  a  distribution  of 
each  increment  of  pressure  along  the  pipe,  this  oscillatory  wave  is 
avoided  and  the  pressure  produced  at, any  instant  during  closure 
(given  by  equation  (7)  is  that  which  is  necessary  to  retard  the 
moving  column  of  water  at  the  rate  at  which  its  velocity  actually 
decreases  at  that  instant  and  can  be  reduced  below  any  assumed 
maximum  allowable  value  by  a  sufficiently  slow, gate  movement. 

When  a  penstock  is  long,  these  oscillatory  waves  become  a 
source  of  great  danger  to  ,the  turbines  and  also  to  the  penstock, 
especially  at  bends.  The  extinction  of  a  velocity  of  4  feet  per 
second  at  a  uniform  rate  in  one  second  in  a  pipe  1,600  feet  in  length 
would  create  a  pressure-head  of  about  200  feet,  or  a  total  longitud- 
inal thrust  on  the  pipe  line  at  each  bend,  and  upon  the  wheel  gate, 
if  24"  in  diameter,  of  abo(ut  20  tons. 

These  dangers  are  further  augmented  by  the  fact  that  several 
waves,  if  succeeding  each  other  by  an  interval  which  is  approxi- 
mately a  multiple  of  the  vibration  period  of  the  pipe,  may  pile  up, 
so  to  speak,  crest  upon  crest  and  cause  a  pressure  which  no  possi- 
ble strength  of  parts  could  withstand. 


Fig.  278. 


214.  Permissible  Rate  of  Gate  Movement. — Gate  movements 
must  be  sufficiently  slow  to  avoid  oscillatory  waves  of  dangerous 
amplitude.  No  general  quantitative  rule  can  be  given  for  the  re- 
quired rate  o;f  movement.  It  can  be  more  rapid  the  shorter  the 
penstock  and  the  smaller  the  velocity  in  the  same.  The  danger 
is  much  smaller  during  opening  than  during  closure  of  a  gate  and 


452       The  Speed  Regulation  of  Turbine  Water  Wheels. 

the  rate  of  gate  .movement  could  well  be  made  much  more  rapid 
in  the  former  than  in  the  latter  case. 

The  rapidity  with  which  a  gate  should  be  opened  is  limited  for 
feeder  pipes  with  an  initial  flat  slope  as  shown  in  Fig.  278. 

Let  h'  be  the  lowest  head  obtained  in  opening  the  gate  at  an  as- 
sumed rate  and  AB,  the  resulting  hydraulic  gradient.  In  case  the 
gate  opens  sov  rapidly  as  to  cause  the  distance,  a,  at  any  point  along 
the  pipe  to  exceed  suction  limit,  the  water  column  m  the  penstock 
will  separate  (the  portio,n  of  the  column  above  A  not  being  able 
to  accelerate  as  rapidly  as  that  below)  and  will  again  reunite  with 
a  severe  hammer  blow.  Failure  to-  observe  this  precaution  probably 
caused  the  destruction  of  the  feeder  pipe  of  the  Fresno,  California, 
power  plant.  The  rate  to  be  used  can  be  chosen  after  a  determina- 
tion, by  the  method  discussed  in  Appendix  A,  of  the  pressures  re- 
sulting from  several  assumed  rates  of  movement.  The  method  is  te- 
dious but  justifiable  in  many  cases. 

215.  Regulation  of  Impulse  Wheels. — It  is  impracticable,  if  not 
impossible,  to  build  a  pipe  line  strong  enough  and  well  enough 
anchored  at  all  points  to  withstand  the  enormous  pressures  and 
longitudinal  thrusts  which  would  result  from  rapid  gate  closures 
in  a  long  closed  penstock  such  as  commonly  used  for  impulse 
wheels.  The  adjustment  of  quantity,  q,  for  changes  in  load%  of 
short  duration  is  hence  impossible  in  such  closed  penstocks  and  the 
expedient  usually  adopted  is  to  "deflect"  the  jet  from  the  wheel  by 
changing  the  direction  of  discharge  of  a  pivoted  nozzle.  This  re- 
quires that  the  "needle  valve"  (See  Fig.  195)  or  gate  maintain  a  jet 
sufficient  to  carry  peak  loads ;  hence  causing  a  waste  of  water  at  all 
other  times.  This  condition  is  commonly  improved  somewhat  by 
adjusting  the  valve  about  once  each  hour  by  means  of  a  slow  motion 
hand  wheel  for  the  maximum  peak  load  liable  to  occur  during  that 
hour. 

An  automatic  governor  has  recently  been  invented  which  moves 
the  needle  valve  or  gate  slowly,  thus  adjusting  for  changes  of  load 
of  long  duration  while  it  still  retains  the  deflector  to  provide  for 
abrupt  changes  in  the  load  curve.  (See  Fig.  282.) 

Another  device  proposed  fo>r  use  in  this  connection  is  a  by-pass 
nozzle  arranged  to  open  as  the  needle  valve  rapidly  closes,  and  then 
automatically  close  again  at  a  rate  sufficiently  slow  to  reduce  the  ex- 
cess pressure  to  safe  limits.  One  advantage  in  favor  of  this  ar- 
rangement is  that  the  jet  would  then  always  strike  the  center  of 
the  buckets  which  is  found  to  considerably  reduce  their  wear. 


Influence  Opposing  Speed  Regulation.  453 

An  automatic  relief  valve  of  hydraulic  or  spring  type  is  nearly 
always  used  but  serves  more  as  an  emergency  valve  to  reduce  water 
hammer  pressures  than  as  a  by-pass  to  divert  water  from  the  wheel 
for  the  purpose  of  governing?  For  this  latter  use  the  spring  type 
of  valve  has  proven  unsatisfactory. 

In  some  cases  the  water  discharged  from  high  head  plants  is  used 
below  for  irrigation  and  must  be  kept  constant,  thus  doing  away 
with  the  necessity  of  varying  the  velocity  in  the  feeder  pipe  for  a 
varying  load. 

Mr.  Raymond  D.  Johnson  proposes  for  these  high  head  plants, 
the  use  of  large  air  chambers  or  "Surge  Tanks,"  placed  near  the 
wheels,  of  a  sufficient  size  so  that  the  governor  can  control  the 
needle  valve  directly,  thus  dispensing  with  the  deflector  and  by- 
pass and  doing  away  completely  with  the  waste  of  water  occa- 
sioned by  their  use.  He  has  derived  formulas  by  which  he  claims  to 
accurately  proportion  these  tanks  for  an  assumed  maximum  allow- 
able range  of  head  fluctuation  or  surge.* 

216.  Influences    Opposing    Speed    Regulation. — Abrupt    changes 
in  the  demand  for  power  of  a  considerable  proportion  of  the  total 
capacity  of  a  plant,  take  place  at  times  in  modern  power  plants. 
Three  causes  tend  to  make  the  change  in  output  of  a  wheel  lag  be- 
hind the  change  in  demand  placed  upon  it;  viz.:  (i)  the  fact  that 
the  governor,  however  sensitive,  does  not  act  until  an  appreciable 
change  of  speed  occurs,  and  then  not  instantly;  (2)   the  fact  that 
some  time  is  required  for  the  readjustment  of  penstock  velocity, 
even  after  the  gate  movement  is  complete ;   (3)   the  necessity  of 
changing  the  velocity,  and  hence  of  overcoming  the  inertia  of  the 
water  in  the  penstock  and  draft  tube  at  each  change  of  load. 

Each  of  these  influences  is  directly  opposed  to  speed  regulation, 
as  will  appear  in  the  succeeding  articles,  since  each  causes  the 
power  supplied  to  a  wheel,  at  time  of  increasing  load,  .to  fall  short 
of  the  demand,  the  deficiency  being  supplied  at  the  expense  of  the 
speed  from  the  kinetic  energy  stored  in  the  rotating  parts.  The  ex- 
pression for  the  total  deficient  work,  i.  e.  footpounds,  is: 

(8)  A  K  =  A  Ki  +  A  K2  +  A  K8 

for  which  see  equations  22  and  23  and  Section  221. 

217.  Change  of  Penstock  Velocity. — Assuming  the  gate   move- 
ment to  take  place  instantly,  we  will  have  the  condition  illustrated 

*  See  "The  Surge  Tank  in  Water  Power  Plants,"  by  R.  D.  Johnson.  Trans. 
Am.  Soc.  M.  E.,  1908. 


454       The  Speed  Regulation  of  Turbine  Water  Wheels. 

in  Figs.  276  or  277,  for  which  equation  7  was  derived  (See  Section 

213).     Solving  equation  (7)  for  -^-  we  have: 

dv         2*  sr 

(9)  Acceleration  —  —r—  =  -f-  X  (accelerating  head)  =  -f-  ha 

Qt  1  1 

The  accelerating  head  as  shown  in  equation  6  is  H  —  h  —  hf.  It 
is  the  general  principles  of  hydraulics  that  the  head  lost  in  flow 
through  any  opening,  pipe,  orifice,  etc.,  varies  as  the  square  of 
velocity. 

It  was  shown  in  Section  160,  Chapter  XIV,  that  the  quantity 
flowing  through  a  turbine  varies  as  the  square  root  of  the  head. 
Remembering  that  the  quantity  is  proportional  to  the  penstock 
velocity,  we  have : 

q        v       Vh 

(10)  -Q  =  y-  =     /TJ >     from  which 

XT  2 

h  = 


V2 

12)  hf  =  (l+f. 


2g 


(is)  -£-:---w     Or 

(14)  hf=4^hF 


From  equation  (6) 

h.  =  H-h-hf  =  H-H'^---hF    -IL      or 

(15)  ha  =  H  —  (H'  +  hF  )^- 

And  from  equation  (5) 

Hence  from  equation  (9) 


dt          1  V2 

The  integration  of  this  equation  as  given  in  Appendix  B  gives 
the  follpwing  equation  for  the  curve  of  velocity  change  in  the  pen- 
stock a  sudden  change  of  gate  opening: 

(18)  Bantilogk't-1 

Bantilogk't  +  1 

As  shown  in  Appendix  —  this  value  of  v  approaches  but  never 
equals  the  value  of  V.  The  form  of  the  curve  for  an  increasing 
velocity  is  shown  in  Fig.  279. 

*  See  Merriman's  Treatise  on  Hydraulics, 


Effect  of  Acceleration  on  Water  Supplied  to  Wheel.       455 

218.  Effect  of  Slow  Acceleration  on  Water  Supplied  to  Wheel. — 
Since  velocity  in  the  penstock,  discharge  of  wheel,  and  loacl 
are  approximately  proportional  to  each  other,  the  ordinates  of 
Fig.  279  may  be  taken  to  represent  loads.  The  load  demand  remains 
at  a  constant  value  v0  from  A  to  B,  where  it  suddenly  increases 
to  YJ,  following  the  line  A  B  C  D  T.  The  supply,  however, 
assuming  an  instantaneous  gate  movement,  follows  the  line 
A  B  D  F.  Now,  the  total  quantity  of  water  supplied  to,  and  hence 


Fig.  279. 

the  work  (not  power)  done  by  the  water  upon  the  wheel,  is  propor- 
tional to  the  area  generated  by  an  ordinate  to  the  latter,  and  the 
demand  upon  the  wheel  to  the  area  generatd  by  the  power  curve. 
The  area  B  C  D  B  therefore  represents  a  deficiency  of  developed 
wrork  which  must  be  supplied  by  the  energy  stored  in  the  rotating 
parts. 

For  practical  purposes  this  area  may  be  assumed  equal  to  the 
area  L  of  the  triangle  B'  C'  D',  where  the  line  B'  D'  is  tangent  to 

the  curve  B  M  D  at  the  point  of  mean  velocity -—o-^ 

The  slope  of  the  line  B'  D'  for  this  mean  velocity  is  readily  ob- 
tained from  equation  17.    Call  it  M,  then 

•pr  _  B'  C'     _  vi  —  vo  _  gH  |~        (v0  +  vi 
C'  D'   ~         T'  "Tl  4V2 


(19) 


and 


456       The  Speed  Regulation  of  Turbine  Water  Wheels. 


(21)  Area  B'C'D'  =  L 


This  value  of  L  is  expressed  in  feet  and  represents  the  deficiency 
of  lineal  distance  moved  by  the  water  column  in  the  penstock.  The 
deficiency  of  supplied  water  in  cu.  feet  is,  hence,  A  L  and  the  de- 
ficiency of  undeveloped  work  is 


(22)  A  K,  -  ALwH  =  -.  (  vi  -  v0)2 

219.  Value  of  Racing  or  Gate  Over-Run.  —  At  D,  Fig.  279,  the 
supply  line  B  D  F  crosses  the  load  line  C  D  E,  and  the  speed  which 
was  lost  from  B  to  D  begins  to  pick  up  again. 

The  necessity  also  for  an  overrun  of  the  governor  is  shown  by 
Fig.  279.  If  the  demand  line  were  A  B  N  F  and  the  gate  opened 
to  the  same  place  as  before,  giving  the  supply  line  B  D  F,  the  sup- 
ply of  power  would  approach,  but  theoretically  never  equal,  the 
demand  and  the  speed  would  hence  never  pick  up  to  normal.  The 


NORMAL    GATE  -  f>  EW  LOAD 


_______  NORMAL    GATE  -   OLD   LOAD  __ 

Fig.  280. 

gate  movement  should  therefore  be  similar  to  that  shown  in  Fig. 
280  in  order  to  give  the  gate  the  small  overrun  which  is  necessary 
to  bring  the  speed  back  to  normal. 

220.  Energy  Required  to  Change  the  ,Penstock  Velocity.—  The 
energy  involved  in  the  change  of  velocity  above  described  results 
in  an  excess  or  deficiency  of  energy  delivered  to  the  wheel  (See  Sec- 
tion 210).  The  amount  of  this  excess  or  deficient  energy  is  readily 
determinable.  The  kinetic  energy  in  foot  pounds  stored  in  the 

moving  column  of  water  is  K2  =  -—     Or 


, 

The  amount  which  must  be  diverted  from  the  wheel  or  dissipated 
when  the  velocity  changes  is  therefore 

(23)  A  K2  =  0.972  Al  (vi2  —  v02) 

In  this  case  it  should  be  taken  as  the  combined  length  of  penstock 
and  draft  tube. 


The  Fly-  Wheel.  457 

This  deficient  energy  must  be  supplied,  or  the  excess  absorbed,  by 
means  of  a  flywheel  or  'the  installation  of  a  stand-pipe  connected 
with  the  penstock  closely  adjoining  the  wheel. 

221.  Effect  of  Sensitiveness  and  Rapidity  of  Governor.  —  Referring 
again  to  Fig.  279,  suppose  the  increase  of  load  to  take  place  at  B'" 
giving  the  load  line  AB"'  C"  E.    After  -an  interval  from  B'"  to  B", 
the  speed  has  dropped  an  amount  depending  upon  the  sensitiveness 
of  the  governor.    The  gate  will  then  begin  to  open  ;  the  velocity  in 
the  penstock  accelerating  meanwhile  along  the  dotted  line  B'"Y. 
The  lack  of  sensitiveness  of  the  governor  has  therefore  added  a  de- 
ficient work  area  of  B'"  B"  C"  C'",  and  the  sluggishness  of  its  mo- 
tion an  additional  area  C"B"  B  C,  approximately.     This  deficiency 
A  K3  can  be  only  roughly  approximated  without  the  detailed  analy- 
sis given  in  Appendix  B. 

222.  The   Fly-Wheel.  —  A  fly-wheel  is  valuable  for  the   storage 
of  energy.    Work  must  be  done  upon  it  to  increase  its  speed  of  rota- 
tion, and  it  will  again  give  out  this  energy  in  being  retarded.    From 
the  laws  of  mechanics  the  number  of  foot  pounds  of  kinetic  energy 
stored  in  a  body  by  virtue  of  its  rotation  is  given  by  the  formula  : 


_2X  3.1416' 
'  ~iW  ~  32~15  X  60* 
(24)  K'  =  .00017  IS2 


The  amount  of  energy  which  must  be  given  to  or  absorbed  from 
the  fly-wheel  in  order  to  change  the  speed  is  : 


(25)  AK'  =  000171  (?02  —  Si2) 

Thus  a  fly-wheel  can  store,  energy  only  by  means  of  a  change  in 
speed.  By  means  of  a  sufficiently  large  moment  of  inertia  the  speed 
change  of  a  fly-wheel,  for  any  given  energy  storage,  A  1C,  can  be  re- 
duced to  any  desirable  limit. 

The  need  of  a  fly-wheel  effect  to  carry  the  load  of  a  hydro-electric 
unit  during  changes  of  gate,  and  while  the  water  is  accelerating  in 
the  penstock  at  an  increase  of  load  has  led  to,  the  development  of  a 
type  of  revolving  field  generator,  whose  rotor  has  a  high  moment  of 
inertia  and  is  therefore  especially  adapted  for  speed  regulation  usu- 
ally making  the  use  of  a  fly-wheel  unnecessary. 

Warren*  has  simplified  the  expression  for  AK'  (See  equation 
25),  substantially  as  follows: 

*  See  "Speed  Regulation  of  High  Head  Water  Wheels,"  by  H.  E.  Warren, 
in  Technology  Quarterly,  Vol.  XX.  No.  2. 


458       The  Speed  Regulation  of  Turbine  Water  Wheels. 

From  equation  (24)  : 

(ae)  |V  =  ^™   =  *;       Hence, 

K2          .0001/  I  02          82 

(9-?\  Ki'-K,'  _  S^-S22         (Si  +  SQ  (Si -SQ 

K/  ~~S?~  tf*' 

Put  Si  —  S2  =  A  S 
and  Kix  —  K2X  =  A  Kr 

For  small  differences  between  S,  and  S2  equation  (27)  becomes 
approximately : 

A     ~LT/  OQ    \y     AG  O    \/     A     C 

(28)  AK        2SXAS   =2XAS       Qr 

JV  (32  *5 

(29)  A  K'  =  ^ 


Or  the  percentage  change  in  speed  is 

(SO)  d  =  100X 


223.  The  Stand-Pipe.  —  The  function  of  the  stand-pipe  is  two- 
fold: (i)  to  act  as  a  relief  valve  in  case  of  excess  pressures  in  the 
penstock  ;  (2)  to  furnish  a  supply  of  energy  to  take  care  of  sudden 
increases  of  load  while  the  water  is  accelerating,  and  to  dissipate  the 
excess  kinetic  energy  in  the  moving  water  column  at  time  of  sudden 
drop  in  load.  For  these  purposes  it  should  be  of  ample  diameter  and 
placed  as  close,to  the  wheel  as  possible. 

The  analytical  determination  of  the  effect  of  a  given  stand-pipe 
upon  speed  regulation  is  very  difficult  if  not  quite  impossible.  Fur- 
thermore, it  is  not  necessary,  since  the  drop  in  effective  head  at  an 
increase  of  load  may  (except  in  the  case  of  maximum  possible  load) 
be  compensated  for  by  an  increase  of  gate  opening,  hence  main- 
taining a  constant  power  and  speed  or  at  least  a  satisfactory  degree 
of  speed  regulation.  Thus  the  action  of  a  stand-pipe  in  storing 
energy  differs  radically  from  that  of  the  fly-wheel  as  the  latter  can 
store  or  give  out  energy  only  by  means  of  a  change  of  speed  in 
the  generating  unit. 

The  determination  of  the  range  of  fluctuation  of  water  level  in  an 
assumed  stand-pipe,  and  the  time  required  for  return  to  normal  level 
for  various  changes  of  load  on  the,  wheel,  will  assist  greatly  in  the 
design  of  the  stand-pipe. 

Fig.  281  shows  the  condition  when  a  stand-pipe  is  used.  Assume 
that  the  wheel  is  operating  under  part  load.  The  water  normally 
stands  a  height  hF  below  the  supply  level.  If  the  load  suddenly  in- 
creases, the  gates  open,  and  the  water  level  begins  to  fall,  thus  caus- 
ing an  accelerating  head  ha  =  H  —  h  --  hf.  Equation  9  then  applies 
as  before,  where  ha  becomes  (h—  cv2). 


The  Stand-Pipe. 


459 


If  the  governor  keeps  step  with  the  change  in  head  by  increasing 
the  gate  opening  to  maintain  a  constant  power  then 


(31) 


q  h  =  qi  hi 

q  (H  —  y)  =  Avi  (H  —  hF  )  =  Avi  (H  —  cvr ) 
_  Avi  (H  —  cvi8) 


or 


H  — y 

The  rate  of  water  consumption  by  the  wheel  at  any  instant  is  q ; 
the  rate  at  which  the  water  is  supplied  by  the  penstock  is  Av;  and 
the  rate  of  rise  or  fall  of  the  water  surface  in  stand-pipe  is  there- 
fore : 

,o2]         dy   __   dh   _  Av  -  q  _  A  T  vi   (H-cvi2)    1 

dF".~dT-      ~F~    "FT  H-y 

The  solutions  of  equations  9  and  32,  which  are  necessary  for 
determining  the  curves  of  variation  of  head  and  velocity,  is  imprac- 


Fig.  281. 


ticable,  if  not  impossible,  hence  a  different  treatment  is  proposed  and 
considered  in  Appendix  C. 

If  q  be  assumed  constant  (=Av1)  during  the  adustment  of  pen- 
stock velocity  and  the  friction  loss,  cv2,  in  the  penstock  be  neglected, 
then  equations  9  and  32  simplify  and  become  integrable.  The  re- 
sulting equations,  showing  the  variations  of  v  and  y,  are  true  har- 
monics or  sine  curves.  The  effect  of  friction  and  governor  action  is 
to  produce  a  damped  or  somewhat  distorted  harmonic  as  discussed 
in  Appendix  C.  Any  change  of  load  thus  starts  a  series  of  wave  like 
fluctuations  of  penstock  velocity  and  stand-pipe  level  which  con- 
tinue until  this  wave  energy  has  been  entirely  expended  in  friction. 


460       The  Speed  Regulation  of  Turbine  Water  Wheels. 

Analogous  to  all  other  wave  motions  these  waves  may  pile  up,  (if 
two  or  more  gate  movements  succeed  each  other  by  short  intervals 
which  are  approximately  multiples  of  the  cycle,  2T)  causing  a  very 
great  flucuation  in  head  and  velocity.  In  fact  by  assuming  a  proper 
combination  and  succession  of  circumstances  no  limit  can  be  as- 
signed to  the  range  of  fluctuation  or  "surge"  which  may  occur.  The 
probable  combination  of  circumstances  which  will  occur  in  any 
plant  depends  largely  .upon  the  character  of  the  load.  Overflows 
from  stand-pipes  due  to  these  surges  have  been  known  to  do  con- 
siderable damage  and  it  is  desirable  to  either  provide  for  this  over- 
flow either  at  the  top  or  by  relief  valves  at  the  bottom,  or  build 
the  stand-pipe  high  enough  to  prevent  it  and  thus  gain  the  addi- 
tional advantage  of  conserving  the  water  which  would  otherwise 
waste. 

If  the  change  of  load  is  assumed  to  occur  when  the  water  is  at 
its  normal  level  then  the  analysis  given  in  Appendix  C  furnishes  the 
following  formulas : 


"A* 


(34) 


(35)  D*-2HD=     -(vi8- 

(36) 

(37) 


The  value  of  T  from  equation  (33)  is  one-half  a  wave  cycle  or 
the  time  required  for  return  to  normal  head  after  a  change  of  load. 
It  is  obtained  by  neglecting  both  friction  and  the  compensating 
effect  of  the  governor.  These  influences  increase  T  in  very  nearly 
the  ratio  that  D  exceeds  Y. 

Y  from  equation  (34)  is  the  maximum  head  fluctuation,  or  maxi- 
mum value  of  y,  also  obtained  by  neglecting  friction  and  governor 
action. 

D  from  equation  (35)  is  the  maximum  drop  in  standpipe  level 
corresponding  to  Y  except  that  governor  action  is  included.  If 
this  value  of  D  is  added  as  shown  in  equation  (36)  to  the  initial 
friction  loss,  cv02,  the  result  agrees  very  closely  with  the  value  of 
the  maximum  drop  D  where  friction  is  included  and  is  much  more 
simple  than  the  more  exact  equation  given  in  Appendix  C. 

A  reasonable  assumption  for  determining  the  probable  maximum 
height  to  which  the  water  will  rise  in  the  stand-pipe  is  that  full 


Predetermination  of  Speed  Regulation.  461 

load  is  instantly  thrown  off  the  unit  when  the  normal  full  load  ve- 
locity vf  exists  in  the  penstock.  This  assumption  leads  to  equa- 
tion (37). 

The  verification  of  these  formulas  and  some  additional  ones  is 
given  in  Appendix  C,  and  an  example  of  their  application  in  sec- 
tion 230. 

224.  The  Air  Chamber. — There  is  a  practical  limit  to  the  height 
to  which  a  stand-pipe  can  be  built.  A  high  stand-pipe  is  also  less 
effective  due  to  the  inertia  of  the  water  in  the  stand-pipe  itself  which 
must  be  overcome  at  each  change  of  load,  thus  introducing  to  a 
lesser  degree  the  same  problem  as  in  a  penstock  without  stand-pipe. 
For  some  such  cases  the  top  of  the  tank  can  be  closed  and  furnished 
with  air  by  a  compressor.    The  design  of  air  chambers  has  been  in- 
vestigated by  Raymond  D.  Johnson.*     An  air  chamber  is  less  effec- 
tive in  equalizing  the  pressure  than  a  standpipe  of  the  same  diam- 
eter. 

225.  Predetermination  of  Speed  Regulation  for  Wheels  Set  in 
Open  Penstocks. — The  influences  which  oppose  speed  regulation 
have  been  partly  discussed.    At  an  increase  or  decrease  of  load  there 
is  a  deficiency  or  excess  of  developed  power  due  to  (i)  the  inability 
of  the  governor  to  move  the  gate  upon  the  instant  that  the  load 
changes;  (2)  the  necessity  of  accelerating  or  retarding  the  water 
in  the  penstock  and  draft  tube  as  previously  discussed.    If  no  stand- 
pipe  is  used,  reliance  must  be  placed  upon  the  fly-wheel  effect  of 
turbine,  generator  and  additional  fly  wheel,  if  necessary,  to  absorb 
or  give  out  the  excess  or  deficiency  of  input  over  output  of  the  plant 
at  this  time. 

The  first  influence  opposed  to  speed  regulation,  that  of  slow  gate 
movement,  is  of  chief  importance  (a)  where  the  plant  is  provided 
with  large  open  penstocks  and  short  draft  tubes ;  (b)  where  an  am- 
ple stand-pipe,  placed  close  to  the  wheel,  and  a  short  draft  tube 
are  used;  (c)  in  the  regulation  of  an  impulse  wheel  where  no  at- 
tempt is  made  to  change  the  velocity  of  water  in  the  feeder  pipe. 
Mr.  H.  E.  Warrenf  has  analyzed  this  case  essentially  as  follows: 
"As  long  as  the  output  from  the  wheel  is  equal  to  the  load,  the 
speed  S  and  kinetic  energy  K'  of  the  revolving  parts  will  remain 
constant.  The  governor  is  designed  to  adjust  the  output  of  the 
wheel  to  correspond  with  the  load,  but  it  cannot  do  this  instanta- 


*  See  Trans,  of  Am.  Soc.  M.  E.,  1908. 

t  See  article  by  H.  E.  Warren  on  "Speed  Regulation  of  High  Head  Water 
Wheels,"  previously  referred  to  in  Section  222. 

28 


462       The  Speed  Regnlation  of  Turbine  Water  Wheels. 

neously.  Consequently,  during  the  time  T  required  to  make  the 
adjustment  of  the  control  mechanism  after  a  load  change  there  will 
be  a  production  of  energy  by  the  water  wheel  greater  or  less  than 
the  load.  The  entire  excess  or  deficiency  will  be  added  to  or  sub- 
tracted from  the  kinetic  energy  of  the  revolving  parts,  and  will  be- 
come manifest  by  a  corresponding  change  in  speed. 

Neglecting  friction  losses,  and  assuming  that  the  power  of  the 
water  wheel  is  proportional  to  the  percentage  of  the  governor  stroke 
and  that  the  movement  of  the  governor  after  a  load  change  is  at  a 
uniform  rate,  the  excess  or  deficient  energy  which  goes  to  or  comes 
from  the  revolving  parts  after  an  instantaneous  change  of  load  from 
L0  to  Lj  is  measured  by  the  average  difference  between  >the  power 
of  the  wheel  and  the  new  load  during  the  time  T",  while  the  gover- 
nor is  moving,  multiplied  by  T"  or  expressed  in  foot  pounds  : 

(38)  A  K'  =  P°~Pl  X  T"  X  550 

From  equation  24  the  kinetic  energy  of  the  rotating  parts  is  : 

K'  =  .00017  IS8 
From  equations  24,  30  and  38 

50X(p0  —  pi)T*X560 

2X  -00017  IS2 

(39)  *  =  81,  000,  000  ^5-  (Po  -  pi) 

226.  Predetermination  of  Speed  Regulation,  Plant  with  Closed 
Penstock.  —  In  this  case  the  rotating  parts  must  absorb  or  deliver 
up  an  amount  of  energy  AK'  (equation  29),  equivalent  to  that  given 
for  AK  in  formula 

(8)  AK  =  AKi+  AK2+  AK3 

where,  from  equation  22, 

(22)  AKl 

M  being  obtained  from  equation 


The  value  of  A  K2  is  obtained  by  equation 

(23)  AK8  =  0.972  Al  (Vi3  —  v02) 

There  is  no  simple  way,  as  discussed  in  section  221,  of  determin- 
ing K3.  It  must  be  estimated  or  analyzed  graphically  as  in  Appen- 
dix C. 

From  equation 

(24)  K'  =  .00017  IS2 


Predetermination  of  Speed  Regulation.  463 

If  R  is  the  proportion  of  this  theoretical  energy  which  is  given  to 
the  rotating  parts  at  a  decrease  in  load,  or  which  the  rotating  parts 
must  give  out  during  an  increase  of  velocity  and  load  then 

(40)  AK'  =RX  AK 

and  we  have  from  equation 

50  X  R  X  A  K 


(30)-  AK'  = 


K' 

50  x  R  X  A  K 


.00017  I 
(41)  5  =  294,000 


RX  AK 


!SS 

Solving  for  I  we  find  the  moment  of  inertia  of  the  rotating  parts, 
which  is  necessary  to  obtain  any  desired  percentage  of  regulation  to 
be 

(42) 


Although  there  can  be  no  doubt  as  to  the  accuracy  of  the  form  of 
equations  41  and  42  yet  their  value  for  other  than  comparative  pur- 
poses depends  upon  the  accuracy  with  which  we  can  estimate  R. 
With  perfect  efficiency  of  the  wheel  under  all  conditions,  R  would 
be  unity,  but  in  actual  cases  R  must  be  determined  by  experiment  or 
by  the  graphical  method  given  in  Appendix  B.  It  will  be  less  for 
decreasing  than  for  increasing  loads  since  the  inefficient  operation 
of  the  wheel  assists  speed  regulation  in  the  former  case,  and  hinders 
it  in  the  latter.  In  addition  to  this  fact,  the  excess  energy  at  a  de- 
crease of  load  can  be  partially  dissipated  through  a  relief  valve,  or 
a  by-pass,  etc.  For  practical  cases  it  is  therefore  necessary  to  in- 
vestigate only  the  case  of  increasing  load. 

A  detailed  analysis  of  a  particular  problem  can  be  made,  as  in 
Appendix  B,  by  which  the  velocity  in  the  penstock,  effective  head, 
power  of  wheel,  speed,  etc.,  can  be  determined  for  each  instant  dur- 
ing the  period  of  adjustment.  From  this  also  the  time  of  return  to 
normal  speed  can  be  determined.  The  method  is  somewhat  tedious, 
but  justifiable  nevertheless. 

227.  Predetermination  '  of  Speed,  Regulation,  Plant  with  Stand- 
pipe.  —  If  the  stand-pipe  is  of  suitable  diameter  and  close  to  the  wheel 
the  speed  regulation  will  approach  that  obtainable  in  open  penstock 
and  as  investigated  by  Warren  in  Section  225.  Otherwise  the  prob- 
lem becomes  that  of  a  plant  with  a  closed  penstock,  of  a  length  equal 
to  that  of  the  draft  tube,  plus  the  penstock  from  stand-pipe  to  wheel. 


464       The  Speed  Regulation  of  Turbine  Water  Wheels. 


228.  Application  of  Method,  Closed  Penstock. — An  example  of 
the  analysis  of  a  problem  in  speed  regulation  is  as  follows : 

Assume  the  48"  Victor  cylinder  gate  turbine,  whose  characteristic 
curve  is  shown  in  Fig.  245,  page  402.  Suppose  it  is  supplied  with 
water  through  a  penstock  whose  diameter  is  8  feet,  jand  whose 
length  combined  with  that  of  the  draft  tube  is  500  feet.  The  head 
is  50  feet  which  for  ^=.664  gives  180  R.  P.  M.  =  S. 

Neglecting  all  losses  of  head  except  that  in  the  turbine,  we  find 
from  the  characteristic  curve  for  various  loads  as  follows : 


Full  load. 

.8  Load 

K  Load. 

M  Load. 

Brake  Hors6  Power 

ll'^O  00 

900 

560  00 

280  00 

Qu&ntity  of  water  p6r  S6C   (  cu   ft 

240  00 

210 

145  00 

97  80 

Velocity  in  Penstock    V. 

4  77 

4  18 

2  88 

1  94 

Efficiency  of  wheel    

82 

754 

68 

505 

The  above  values  will  be  considered  as  applying  to  the  entire 
plant  since  the  loss  in  the  penstock  is  small  in  this  case. 

Assume  the  load  to  increase  suddenly  from  one  quarter  load  to 
0.8  load,  while  the  gate  at  the  same  time  opens  to  full  load  posi- 
tion. The  nujmber  of  foot  pounds  of  work  which  must  be  done  to 
accelerate  the  water  from  a  velocity  of  1.94  feet  per  second  to  4.18 
feet  per  second  is  found  from  equation  23  to  be 
AK2  =0.972  Al  K3—  v02) 

=  0.972  X  50.3  X  500  (4.182  —  1.942) 
=  0.972  X  50.3  X  500  X  13.73 
=  335,000  foot  pounds. 

Referring  to  section  226,  p.  462,  to  find  the  amount  of  deficient 
work  due  to  insufficient  supply  of  water  we  have 


£ 

From  equation  19,  section  226 

32.15X50 


500         V         4  X  4. 
-  32.15X50 
500 

=  2.88 


From  equation  22, 


-•MXJ^^.^. 

=  187, 000  foot  pounds. 


Predetermination  of  Speed  Regulation.  465 

The  total  deficiency  for  which  formulas  have  been  derived  is 
hence, 

AK  —  AKj  +  K2  +  (AK3  undeterminable) 
=  335,000  +  137,000 
=  472,  000  +  ft  Ibs. 

By  means  of  the  detailed  graphical  analysis  given  ,in  Appendix 
B  this  deficiency  is  found  to  be  600,000  foot  pounds  for  gate  move- 
ment in  one-half  second  showing  that  the  estimated  value  should 
have  been  increased  in  this  case  by  12.7  per  cent.  (R  =  1.127)  to 
compensate  for  neglecting  the  effect  of  slow  (%  second)  gate  move- 
ment, or  K3.  It  must  be  remembered  that  this  quantity,  AK,  is 
the  deficiency  of  ^theoretical  hydraulic  work  done  upon  the  wheel. 
For  reasons  discussed  in  Appendix  B,  it  will,  however,  be  found  to 
differ  but  slightly  from  the  deficiency  of  wheel  output,  in  this  case 
586,000  ft.  pounds. 

To  determine  the  speed  regulation  which  can  be  obtained,  as- 
sume a  generating  unit  whose  rotor  has  a  fly-wheel  effect,  or  mo- 
ment of  inertia,  I,  of  1,000,000  ,lbs.  at  one  ft.  radius.  The  normal 
speed  S  =  180,  AK  =  472,000  ft.  Ibs.,  and  R  (in  general  to  be  esti- 
mated, but  in  this  case  obtained  by  the  graphical  method  given  in 
Appendix  B,  is  1,127.  Therefore  from  equation  (43) 

d  -  994  000  1'127  X472-000  -  5  42* 
y4'°UU  1,000,  000X180*- 

If  a  fly-wheel  is  to  be  designed  for  a  given  regulation  say  4  per 
cent.,  then  the  required  moment  of  inertia  of  same  is,  from  equa- 
tion (42). 

I  =  294,  000  ^- 


I  ='1,355,  000  ft.2  Ibs. 

229.  Application  of  Method,  Open  Penstock.  —  As  the  penstock 
and  draft  tube  are  shortened,  the  excess  or  deficient  energy  area, 
A  K3,  .obtained  during  the  gate  movement  becomes  an  increasing 
proportion  of  the  whole  until  for  a  large  open  penstock  and  short 
draft  tube  the  developed  power  ceases  to  lag  and  follows  practically 
the  same  law  of  change  as  the  gate  opening.  The  estimation  of 
excess  i'or  deficient  energy,  and  consequently  of  speed,  is  then  very 
simple  by  means  of  Mr.  Warrens  equation  (39).  For  illustration: 
assume  the  same  wheel  as  in  the  preceeding  section,  obtaining  the 
outputs  of  280  H.  P.=P0  at  one-fourth  load  and  1120  H.  P.=  Pl  at 


466       The  Speed  Regulation  of  Turbine  Water  Wheels. 

full  load,  as  in  the  other  installation.     Assume  the  same  moment 
of  inertia  1,000,000  and  that  the  gate  movement  takes  place  in  % 
second  as  before.    Then  T"=  %  ;  S  =  180. 
This  gives 

t  =  81.000.0001>000|  ™x  18Q2  (1120  -  280)  =  1.05* 

This  is  a  much  closer  regulation  than  obtained  with  the  long  pen- 
stock. 

230.  Application  of  Method,  Plant  with  Stand-pipe.  —  Assume  a 
plant  where  the  wheels  develop  39,000  H.  P.  under  375  head,  thereby 
requiring  about  noo  cu.  ft.  of  water  per  second  (assuming  83  per 
cent,  efficiency  of  the  wheels).  Assume  this  water  is  supplied 
through  four  7'  pipes  about  4800  feet  long,  requiring  a  velocity  in  the 
feeder  pipes  at  full  load  of  about  7.15  feet.  Suppose  four  pipes  all 
connected  at  the  lower  end  to  a  stand-pipe  30  feet  in  diameter.  If  a 
sudden  load  change,  of  about  one  third  of  the  total  is  to  be  provided 
for  this  would  require  an  ultimate  change  of  velocity  in  the  penstock 
from  about  4.76  feet  per  sec.  at  two^thirds  load  to  7.15  feet  at  full 
load,  or  v0  =  4.76,  and  v±  =  7.15.  Now, 

A  =  4  X  *-=  154  sq.  ft, 


From  equation  33  the  time  required  for  return  to  normal  head,  or 
the  half  period  of  oscillation,  is 


T  = 


This  would  perhaps  be  increased  to  nearly  100  seconds,  due  to  the 
use  of  additional  water  during  this  period  of  low  head,  as  discussed 
in  Appendix  C,  but  the  value  82  should  be  used  in  equation  35. 

Equation  34  gives  for  the  drop  in  water  level  in  the  stand-pipe, 


Y  =  J154  X  480Q      (7.15-4.76) 
^707  X  32.15 

=1/3275  X  2.39  =  13.6  feet. 
The  more  exact  equations,  35  and  36,  give  for  D  and  D, 

i§gg(7.l5^-4.762)+37f  *82(7- 


D2  —  750  D  +  11,120  =  0 


Governor  Specifications.  467 

Solving  this  quadratic  equation  gives 

D  -  750  —  T/7502  —4  X  11,120 

75Q-719 


Qr 


=  15.5  feet 


Db  =  15.5  +  c  X  4.762  =  15.5  +  .176  X  4.76s  =  19.5  feet 

No  attempt  will  be  made  'to  estimate  the  greatest  drop  in  level 
which  might  occur,  due  to  an  addition  of  waves. 

231.  Governor  Specifications.  —  The  present  practice  of  requiring 
the  governor  builder  to  guarantee  the  speed  regulation  of  a  plant, 
in  the  design  of  which  he  has  had  no>  voice,  without  even  giving 
him  the  necessary  information  regarding  the  hydraulic  elements 
which  are  considered  in  this  chapter  is  wrong.  It  is  partly  the  out- 
growth of  the  modern  tendency  to  specialize,  but  perhaps  more 
largely  due  to  a  lack  of  understanding  on  the  part  of  the  engineer  of 
the  nature  of  the  problem,  and  a  resulting  desire  to  shift  the  respon- 
sibility for  results  upon  some  one  else  who  is  better  informed  upon 
the  subject  and  thus  protect  results  financially  as  well  as  save  his 
own  reputation  in  case  of  failure. 

Governor  specifications  should  call  for  a  guarantee  of  the 

(a)  Sensitiveness  or  per  cent  load  change  which  will  actuate  the 
governor  ; 

(b)  Power  which  the  governor  can  develop,  and  force  which  it 
can  exert  to  move  the  gates  ; 

(c)  Rapidity  with  which  it  will  move  the  gates  ; 

(d)  Anti-racing  qualities,  such  as  number  of  gate  movements  re- 
quired to  adjust  for  a  given  load  change  (See  figure  280),  or  per- 
cent. over-run  of  the  gate,  etc. 

(e)  General  requirements  of  material,  strength,  durability,  etc. 
Beyond  this  point  the  governor  designor  has  no  control.     The 

engineer  can,  however,  by  choosing  a  generator  whose  rotor  has  a 
high  moment  of  inertia  (which  quantity  should  be  stated  in  tenders 
for  supplying  the  generators),  by  the  addition  of  a  fly-wheel,  if 
necessary  ;  by  the  construction  of  a  stand-pipe  ;  by  means  of  a  re- 
lief valve,  and  very  largely,  also,  by  the  general  design  of  the  pen- 
stocks, draft  tubes,  etc.,  greatly  improve  the  governing  qualities, 
and,  in  fact,  reduce  the  speed  variation  to  any  desirable  limit  which 
the  nature  of  load  to  be  carried,  magnitude  of  load  changes  antici- 
pated, and  economy  of  first  cost  will  warrant. 


468       The  Speed  Regulation  of  Turbine  Water  Wheels. 


LITERATURE. 

TURBINE    REGULATION. 

1.  Williams,  Harvey  D.    A  New  Method  of  Governing  Water  Wheels.     Sib. 

Jour,  of  Engng.     March,  1896. 

2.  Electric  Governors.    Eng.  News,  1896,  vol.  1,  p.  276. 

3.  Parker,  M.  S.    Governing  of  Water  Power  Under  Variable  Loads.     Trans. 

Am.  Soc.  C.  E.    June,  1897. 

4.  Regulation  of  Wheels.    The  Chavanne  Nozzle  Regulator.     Mining  &  Sci- 

entific Press,  Oct.  30,  1897. 

5.  Knight,  Samuel  N.    Water  Wheel  Regulation.     Jour,  of  Elec.    Nov.,  1S97. 

6.  Replogle,  Mark  A.    Speed  Government  in  Water-Power  Plants.    Jour.  Fr. 

Inst.,  vol.  145,  p.  81,  Feb.,  1898. 

7.  Regulation   of   Water   Wheels    under   High   Pressure.    Pioneer    Electric 

Power  Co.'s  Wheels.    Eng.  Rec.,  Feb.  5,  1898. 

8.  Garratt,  Allan  V.    Elements  of  Design  Favorable  to  Speed  Regulation. 

Eng.  News,  1898,  vol.  2,  pp.  51-159. 

9.  Modern  Practice  in  Water  Wheel  Operation.    Elec.  World,  May  5,  1900. 

10.  Cassel,  Elmer  F.    Commercial  Requirements  of  Water-Power  Governing. 

Eng.  Mag.,  Sept.,  1900. 

11.  Garratt,  Allan  V.    Speed  Regulation  of  Water  Power  Plants.    Cassier's 

Magazine,  May,  1901. 

12.  A  Water-Wheel  Governor  of  Novel  Construction.    Eng.  News,  Nov.  13, 

1902. 

13.  Thurso,  J.  W.    Speed  Regulation  in  Water  Power  Plants.    Eng.  News, 

1903,  vol.  1,  p.  27. 

14.  Governing  Impulse  Wheel  by  an  Induction  Motor.  Eng.  News,  1903,  vol.  1, 

p.  246. 

15.  Garratt,  Allan  V.    Speed  Regulation  of  Water  Power  Plants.    Elec.  Age, 

May,  1904. 

16.  Goodman,    John.    The    Governing   of    Impulse   Water    Wheels.    Engng., 

Nov.  4,  1904. 

17.  Church,   Irving   P.    The   Governing   of   Impulse   Wheels.     Eng.   Record, 

Feb.  25,  1905. 

18.  Gradenwitz,  Alfred.    The  Bouvier  Governor  for  Water  Turbines.    Mach. 

N.  Y.    June,  1905. 

19.  Henry,  Geo.  J.,  Jr.    The  Regulation  of  High-Pressure  Water-wheels  for 

Power  Transmission  Plants.    Am.  Soc.  of  Mech.  Engrs.    May  1, 
1906. 

20.  Replogle,  Mark  A.     Some  Stepping  Stones  in  the  Development  of  a  Mod- 

ern Water-Wheel  Governor.    Am.  Soc.  Mech.  Engrs.    May,  1906. 

21.  Buvinger,   Geo.   A.    Turbine   Design   as   Modified  for   Close   Regulation. 

Am.  Soc.  of  Mech.  Engrs.    May,  1906. 

22.  Lyndon,  Lamar.    A  New  Method  of  Turbine  Control.    Proc.  Am.  Inst.  of 

Elec.  Engrs.    May,  1906. 


Literature.  469 


23.  Water  Wheel  Governors.    Elec.  World.     June  30,  1906. 

24.  A  New  Water  Wheel  Governor.     Eng.  Rec.  Current  News  Sup.    July  14, 

1906. 

25.  Warren,  H.  E.     Speed  Regulation  of  High  Head  Water  Wheels.    Tech. 

Quar.    Vol.  20,  No.  2. 

26.  Johnson,  R.  D.     Surge  Tanks  for  Water  Power  Plants,  Trans.  Am.  Soc.  M. 

E.    1908. 


CHAPTER  XIX. 

THE  WATER  WHEEL  GOVERNOR. 

232.  Types  of  Water  Wheel  Governors. — In  all  reaction  turbines 
and  in  all  impulse  turbines,  with  the  exception  of  tangential  wheels, 
the  governor  affects  regulation,  i.  e.  controls  the  output,  and  hence 
the  speed  of  the  wheel,  by  opening  or  closing  the  regulating  gates, 
thus  varying  the  amount  of  water  supplied  to  the  wheel.  In  tan- 
gential wheels,  under  high  head,  this  method  of  control,  for  obvious 
reasons  (See  section  215),  becomes  difficult  and  in  extreme  cases 
impossible  and  in  such  cases  the  governor  must  be  arranged  to  af- 
fect regulation  by  the 'deflection  of  the  jet  from  the  bucket.  (See 
Fig.  282). 


Fig.  282.— Governing  Impulse  wheel  with  Automatic  Needle  and  Deflecting 
Nozzle   (after  Warren). 

The  force  required  to  move  the  turbine  gates  is  large  (sometimes 
50,000  Ibs.  or  more)  and  it  is  therefore  evident  that  they  cannot  be 
moved  by  the  direct  action  of  the  centrifugal  ball  governors,  as  with 
steam  engines,  but  must  be  moved  by  a  "relay." 

The  relay,  as  its  name  implies,  is  a  device  for  transmitting  energy 
from  a  source  of  energy  independent, —  as  to  quantity — of  the  cen- 
trifugal governor  balls  but  controlled  by  them  in  its  application. 


Types  of  Water  Wheel  Governors. 


471 


If  the  relay  is  of  "mechanical  type"  the  power  required  to  operate 
it  and  the  gates  is  transmitted,  when  needed,  from  the  wheel  by 
means  of  shafts,  gears,  friction-clutches,  belts  and  pulleys  or  other 
mechanical  devices.  In  mechanical  governors  the  flyballs  may 
actuate  pawls,  friction  gears  or  other  mechanical  devices  which  will 
bring  the  relay  into  action. 


Pig.  283. — Woodward  Standard  Governor. 

If  the  relay  is  of  the  hydraulic  type,  it  usually  consists  of  a  piston 
connected  by  some  mechanical  device  to  the  gate  rigging  and  moved 
by  means  of  the  hydraulic  'pressure  of  water  taken  from  the  pen- 
stock, or  other  source,  or  by  oil  supplied  under  high  pressure  from 
a  reservoir.  The  pressure  of  the  oil  in  the  reservoir  is  maintained 
by  compressed  air  supplied  by  power  taken  from  the  wheel  itself. 
The  oil  thus  used  in  moving  the  piston  is  exhausted  into  a  receiver 
from  which  it  is  pumped  back  into  the  supply  reservoir.  The  hy- 
draulic relay  is  commonly  controlled  by  the  ball  governor  through 


472 


The  Water  Wheel  Governor. 


the  medium  of  a  small  valve  which  by  its  motion  either  admits  the 
actuating  water  (or  oil)  directly  to  the  cylinder  or  to  a  secondary 
piston  controlling  a  larger  admission  valve. 

Electrical  methods  of  actuating  the  relays  controlled  by  means 
•of  governor  balls  have  been  used  to  some  extent  but  are  not  nearly 
so  common  as  mechanical  or  hydraulic  devices. 


Pig.  284. — Diagramatic  Section  of  Woodward  Simple  Mechanical  Governor. 

233.  Simple  Mechanical  Governors. — Fig.  283  is  a  view  and  Fig. 
,284  a  diagramatic  section  of  a  simple  mechanical  governor  of  the 
Woodward*  Standard  type.  On  the  upright  shaft  are  two  frictioin 
pans  (a  and  b).  (See  also  Fig.  287).  These  pans  are  loose  on  the 
shaft,  the  upper  one  being  supported  in  position  by  a  groove  in  the 
"hub  and  the  lower  one  by  an  adjustable  step-bearing.  Between 
these  pans,  and  beveled  to  fit  them,  is  a  double-faced,  friction  wheel 
(c)  which  is  keyed  to  the  shaft.  This  shaft  and  friction  wheel  run 

*Woodward  Governor  Co.,  Rockford,  111. 


Anti-Racing  Mechanical  Governors.  473, 

continuously  and  have  a  slight  endwise  movement.  They  are 
supported  by  lugs  on  the  ball  arm  and  therefore  rise  and  fall  as  the 
position  of  the  balls  varies  with  the  speed. 

When  the  speed  is  normal,  the  inner  or  friction  wheel  revolves 
freely  between  the  two  outer  wheels  or  pans  which  remain  station- 
ary. When  a  change  of  speed  occurs,  the  friction  wheel  is  brought 
against  the  upper  or  lower  pan  as  the  speed  is  either  slow  or  fast. 
This  causes  the  latter  to  revolve  and,  by  means  of  the  bevel 
gearings,  turn  the  gates  in  the  proper  direction  until  the  speed  is 
again  normal.  As  the  gate  opens,  the  nut  (d)  travels  along  the 
screw  (e)  which  is  driven  through  gearing  by  the  main  governor 
shaft  and  as  the  gate  reacts,  the  nut  (d)  coming  in  contact  with 
the  lever  (f)  throws  the  vertical  shaft  upward  and  the  governor  out 
of  commission. 

This  type  of  governor  may  be  used  to  advantage  where  the 
water  wheels  operate  a  number  of  machines,  connected  to  a  main 
shaft  and  where,  in  consequence,  the  friction  or  constant  load  is 
a  considerable  percentage  of  the  total  load.  In  such  cases  the 
changes  in  load  may  not  ibe  a  large  percentage  of  the  total  load 
and  the  temporary  variations  in  speed,  which  occur  at  times  of 
changes  of  load,  may  not  be  of  sufficient  importance  to  necessitate 
the  installation  of  a  quick  acting  governor. 

When  the  water  wheel  is  direct  connected  tora  single  machine, 
and  the  friction  load  is  comparatively  small,  the  relative  change  in 
load,  and  the  consequent  possible  changes  in  speed,  is  much  larger. 

In  such  cases  the  type  of  governor  above  shown  will  result  in 
a  serious  hunting  or  racing  (See  Section  211)  of  the  wheel  during 
considerable  changes  of  load,  and  in  unsatisfactory  regulation.  In 
such  cases  governors  with  compensating  or  anti-racing  devices 
must  be  used  for  satisfactory  regulation. 

234.  Anti-Racing  Mechanical  Governors. — The  Woodward  Com- 
pensating Governor. — Fig.  285  is  a  view  and  Fig.  286  is  a  dia- 
gramatic  section  of  a  Woodward  vertical  mechanical  governor  of 
the  compensating  type. 

In  the  simple  Woodward  governor  (See  Figs.  283  and  284)  the 
power  necessary  to  actuate  both  the  centrifugal  governor  balls  and 
the  relay  is  transmitted  through  a  belt  to  a  single  pulley,  P.  In  the 
Woodward  compensating  type  of  governor  the  relay  is  operated 
in  a  similar  manner  by  ;a  single  pulley,  P,  while  the  centrifugal 
governor  balls  are  actuated  by  an  independent  pulley,  q,  having  an 
independent  belt  connected  to  the  wheel  shaft  or  to  some  other  re- 


474 


The  Water  Wheel  Governors. 


volving  part  connected  therewith.  From  the  driving  pulley,  q, 
power  is  transmitted  to  the  governor  balls  through  a  shaft  and 
gearing.  The  shaft  supporting  the  centrifugal  governor  balls 
is  hollow,  and  on  the  ball-arms  are  two  lugs  which  connect  with  a 


Fig.  285. — Woodward  Compensating  Governor. 

spindle  (f),    which  therefore  rises  and  falls  as  the  positions  of  the 
governor  balls  vary  with  the  speed. 

The  movement  of  the  centrifugal  governor  balls  causing  the 
spindle,  f,  to  rise  and  fall  changes  the  position  of  the  tappet  arm, 
g,  to  which  it  is  connected,  and  causes  one  or  the  other  of  the  two 
tappets,  tt',  to  engage  a  double-faced  cam,  h.  This  cam  is  contin- 
uously rotated  by  means  of  the  pulley  above  it,  driven  by  a  belt  con- 
nected with  the  main  vertical  shaft  of  the  relay.  The  tappets  are 


Anti-Racing  Mechanical  Governors. 


475 


connected  to  a  common  suspension  arm  to  which  the  vertical  spin- 
dle, f,  is  attached.  The  suspension  arm  is  hinged  to  the  lever  arm,  j. 
The  lever  arm  is  connected  to  the  shaft,  K,  which  can  be  rotated 
on  its  bearings  and  which  is  connected  with  a  tension  rod,  1,  by  an 
eccentric  at  the  bottom.  The  tension  rod,  1,  is  in  turn  connected  by 


Fig.  286. — Diagramatic  Section  of  Woodward  Vertical  Compensating  Mechan- 
ical Governor, 

a  lever,  m,  with  the  vertical  bearing,  e,  on  which  the  main  shaft  of 
the  friction  cone  rests.  This  bearing  is  movable  around  the  ful- 
crum, n,  and  is  counterbalanced  by  an  arm  and  weight,  u. 

When  either  of  the  tappets  engages  the  rotating  cam,  the  resulting 
movement  turns  the  rocker  shaft,  K,  and,  through  its  connection, 
raises  or  lowers  the  vertical  bearing,  e,  which  causes  the  friction 
wheel,  c,  to  engage  either  the  upper  or  the  lower  of  the  friction 
pans,  a  and  b,  as  in  the  case  of  the  simple  governor. 

The  compensating  or  anti-racing  mechanism  is  just  below  the 
rotating  cam.  It  is  essentially  alike  in  all  of  the  Woodward  com- 
pensating types  of  governors  and  is  described  in  the  governor  cata- 
logue as  follows : 


476  The  Water  Wheel  Governor. 

"On  the  lower  end  of  the  cam  shaft  is  a  friction  disc,  r,  (Fig.  286) 
which  rests  on  a  rawhide  friction  wheel  on  a  diagonal  shaft.  The 
hub  of  the  friction  wheel  is  threaded  and  fits  loosely  on  the  diagonal 
shaft  which  is  normally  at  rest.  The  effect  of  the  continually 
rotating  friction  disc  upon  the  rawhide  wheel  is  evidently  to  cause 
it  to  travel  along  the  threaded  diagonal  shaft  to  the  center  of  the 
disc.  When  the  governor  moves  to  open  or  close  the  gate,  the 
diagonal  shaft,  which  is  geared  to  it,  is  turned  and  the  friction  wheel 
is  caused  to  travel  along  the  shaft  away  from  the  center  of  the  disc 


Fig.  287. — Friction  Cone  and  Pans  of  Woodward  Governor. 

and  thus  raise  or  lower  the  cam  shaft  so  as  to  separate  the  cam  from 
the  tappet  which  is  in  action,  before  the  gate  has  moved  too  far, 
thus  preventing  racing.  As  soon  as  the  gate  movement  ceases  the 
disc  causes  the  friction  wheel  to  return  to  the  center  of  the  disc 
along  the  threaded  shaft." 

To  prevent  the  governor  from  straining  when  the  gate  is  fully 
open  or  closed,  suitable  cams  are  mounted  on  the  stop  shaft. 
"When  the  gates  are  completely  opened,  the  cam  engages  the  speed 
lever  and  holds  it  down  so  that  it  cannot  raise  the  lower  tappet 
sufficiently  to  engage  the  revolving  cam ;  this  does  not,  however, 
interfere  with  the  upper  tappet,  to  prevent  the  closing  of  the  gates, 
should  the  conditions  demand.  The  closed  gate  stop  acts  in  a  sim- 
ilar manner  on  the  upper  tappet  but  does  .not  interfere  with  the 
lower  tappet  being  engaged,  should  the  conditions  demand  that  the 
gate  be  opened.  In  addition  to  these  stops,  the  governor  is  pro- 
vided with  a  safety  stop  whose  function  is  to  immediately  close  the 
gates  should  the  speed  governor  stop  through  breakage  of  the  belt 
or  any  other  cause." 


The  Woodward  Governor. 


477 


235.  Details  and  Applications  of  Woodward  Governors. — Fig.  287 
shows  the  construction  of  the  friction  gearing  of  the  Woodward 
Mechanical  Governor.  In  the  inner  friction  driving  cone,  corks 
are  inserted  in  holes  drilled  in  the  rim  and  these  are  ground  off  true 
so  that  they  project  about  one-sixteenth  inch.  This  seems  to  give  a 
very  reliable  friction  surface  not  readily  affected  by  either  water  or 


Fig.  288. — Woodward  Horizontal  Compensating  Mechanical  Governor  at  Hy- 
dro-Electric Plant  of  U.  S.  Arsenal,  Rock  Island,  111. 


oil,  and  it  is  claimed  to  be  superior  to  either  leather  or  paper  for 
this  purpose.  In  order  to  cause  the  friction  wheel  to  engage 
smoothly  and  noiselessly,  a  plunger  attached  to  the  shaft,  just 
below  the  inner  friction  wheel,  fits  rather  closely  into  a  dash-pot 
formed  in  the  lower  pan. 

Fig.  288  shows  a  horizontal  compensating  type  of  Woodward 
governor  as  installed  to  control  the  gates  of  the  turbines  in  the  Hy- 
draulic Power  Plant  of  the  U.  S.  Arsenal  at  Rock  Island,  Illinois. 
The  cables  shown  at  the  back  of  the  cut  operate  the  gates  of  the 
turbine.  On  the  gate  shafts  of  the  latter  are  sheave  wheels  to  which 
the  cables  are  attached.  These  sheave  wheels  are  fitted  with 
29 


478 


The  Water  Wheel  Governor. 


clutches  so  that  any  gate  may  be  disconnected  from  the  governor. 
Each  gate  is  provided  with  an  indicator  showing  its  position  This 
provides  means  of  coupling  properly,  after  being  disconnected, 
without  closing  the  gates  of  the  other  wheels.  Each  governor  is 
arranged  to  control  six  turbines,  belonging  to  two  different  units. 
Two  belts  are  provided  so  as  to  drive  from  either  unit.  The  gover- 


Fig.  289. — Lombard-Replogle  Mechanical  Governor. 

nor  can  thus  be  used  to  control  three  wheels  on  either  side  or  all 
six  when  the  two  units  are  running  in  multiple. 

236.  The  Lombard-Replogle  Mechanical  Governor.* — Fig.  289 
shows  a  Lombard-Replogle  mechanical  governor.  The  principles 
of  operation  of  this  governor  are  better  illustrated  in  the  diagram, 
Fig.  290. 

In  the  diagram  A  is  a  spherical  pulley  with  its  shaft  turned  down 
and  threaded  as  at  X.  B  and  B  are  revolving  concave  discs  lined 
with  leather  which  are  continuously  revolving  in  opposite  direc- 
tions. C  and  C  are  lignum  vitae  pins  flush  with  the  leather.  D 
and  D  are  compression  springs  for  controlling  the  pressure  between 
the  disks  and  the  sphere.  When  the  spherical  pulley  A  is  shifted 
from  its  central  position  in  the  line  of  its  axis,  the  springs  are 

*The  Lombard-Replogle  Governor  Co.,  Akron,  Ohio. 


The  Lombard-Replogle  Mechanical  Governor. 


479 


tightened  automatically,  causing  increased  traction  as  the  smaller 
diameters  of  the  sphere  engage  the  larger  diameters  of  the  disc. 
E  and  E  are  the  centrifugal  governor  balls  so  poised  as  to  require 
the  weight  of  the  pulley  A  to  balance  them  at  normal  speed.  F  is  a 
loose  collar  to  allow  independent  revolution  of  the  balls  EE.  G 
is  the  point  of  connection  between  A  and  the  gates  or  valve  rigging 
of  the  wheel  to  be  governed.  X  is  the  compensating  device,  and  is 


orernor  Ball 


Fig.    290. — Diagram   of   Lombard-Replogle    Mechanical    Governor. 

for  the  purpose  of  reducing  and  controlling  racing.  Z  is  a  sta- 
tionary spindle  or  connecting  link  between  the  collar  F  and  the 
threaded  shaft  or  pulley  A.  Z  is  only  stationary  in  reference  to 
revolution,  as  it  rises  or  falls  with  the  variations  of  the  governor 
balls. 

The  spherical  pulley  A  is  normally  at  test  while  the  discs  BB  are 
continually  revolving.  A  movement  of  the  governor  balls  raises 
or  lowers  the  shaft  so  that  the  spherical  discs  rotate  the  pulley. 

The  greater  the  displacement  of  the  shaft  the  more  rapid  the 
revolution  since  the  circle  of  contact  on  the  disc  is  increased.  The 
rotation  of  the  spherical  pulley  A  either  shortens  or  lengthens 
the  distance  to  collar  F  by  means  of  thread  X.  "This  shortening 
causes  A  to  be  pulled  back  to  the  disc  centers,  thereby  cutting  the 
governor  out  of  action"  and  preventing  the  gates  from  moving 
too  far  or  racing. 


480 


The  Water  Wheel  Governor. 


Essential  Features  of  an  Hydraulic  Governor.  481 

237.  Essential  Features  of  an  Hydraulic  Governor. — The  essen- 
tial features  of  an  hydraulic  water  wheel  governor  are : 

1.  A  tank  for  storing  oil  under  air  pressure. 

2.  A  receiver  tank  for  the  collection  of  oil  used  by  the  governor. 

3.  A  power  pump  driven  from  the  water  wheel  shaft. 

4.  A  hydraulic  power  cylinder  for  operating  the  gates. 

5.  A  sensitive   centrifugal  ball   system   for  controlling  a  valve 
which  either  admits  oil  directly  to  the  power  cylinder  or  to  an  inter- 
mediate relay  cylinder  the  piston  of  which  operates  the  admission 
valve  to  the  power  cylinder. 

6.  An  anti-racing  or  compensating  mechanism. 

The  power  pump  is  continually  using  power  from  the  wheel  to 
pump  the  oil  from  the  receiver  back  to  the  pressure  tank  thus 
gradually  storing  the  energy  which  is  used  intermittently  to  oper- 
ate the  gates. 

Fig.  291  illustrates  the  Lombard  Type  "N"  Governor  and  shows 
-clearly  the  relations  of  the  various  parts  of  an  hydraulic  governor. 

The  centrifugal  governor  balls  are  connected  by  belt  to  the  wheel 
shaft.  These  balls  control  a  small  primary  or  pilot  valve  of  the 
cylinder  type  which  admits  oil  from  the  large  pressure  tank  under 
about  200  pounds  pressure  into  one  side  of  a  cylinder  where  its  pres- 
sure is  exerted  against  one  of  two  plungers.  These  plungers  control 
a  large  valve,  also  of  the  cylinder  type,  which  admits  oil  from  the 
pressure  tank  to  one  or  the  other  side  of  the  power  piston.  The 
rectilinear  motion  of  the  piston  is  converted,  by  rack  and  pinion,  into 
rotary  motion  for  transmission  to  the  wheel  gates.  The  oil  used 
for  operating  the  power  pistons  and  the  plungers  of  the  relay  is 
•exhausted  into  the  vacuum  tank  from  which  it  is  pumped  back  into 
the  pressure  tank  by  means  of  the  power  pump  shown  at  the  left 
which  is  driven  by  belt  from  the  wheel  shaft.  The  speed  variation 
necessary  to  actuate  the  governor  depends  upon  the  lap  of  the  pilot 
valve  and  is  adjustable. 

238.  Details  of  Lombard  Hydraulic  Governor. — The  details  of 
the  Lombard  Type  N  Governor  are  best  shown  by  the  enlarged 
view  of  the  upper  portion  of  the  governor  (Fig,  292)  and  by  the  sec- 
tion of  the  relay  valve  (Fig.  293).    The  following  description  of  the 
•operation  of  this  governor  is  taken  from  the  Directions  for  Erecting 
and  Adjusting  Governors.* 

"The  oil  from  the  pressure-tank  is  supplied  to  the  working  cyl- 
inder 62  through  the  large  relay-valve  106,  arranged  to  discharge 

*PubHshel  by  The  Lombard  Governor  Co.,  Ashland,  Mass. 


482 


The  Water  Wheel  Governor. 


or  exhaust  oil  directly  and  rapidly  into  or  from  either  end  of  the 
cylinder.  The  relay-valve  106,  through  the  hydraulic  system  con- 
nected therewith,  is  under  the  simultaneous  control  of  the  reg- 
ulating-valve 14  and  the  displacement-cylinder  107-  This  is 


10 


Fig.  292. — Upper  Portion  of  Lombard  Type  N  Governor. 

brought  about  in  the  following  manner.  The  relay- valve  A 
(See  Fig.  293)  is  moved  hydraulically  by  plungers  B  and 
C  contained  within  cylinders  D  and  E  forming  parts  of 
the  relay-valve  heads  F  and  G.  Plunger  B  has  about 
one-half  the  area  of  plunger  C,  consequently  plunger  C  can  over- 
power plunger  B.  if  the  pressure  in  cylinders  E  and  D  is  nearly 


The  Lombard  Governor. 


483 


equal.  The  cylinder  D  is  permanently  in  communication  with  the 
main  pressure  supply  through  the  pipe  H  which  also  furnishes  liq- 
uid to  the  regulating-valve  14.  Therefore  the  tendency  of  plunger 
B  is  always  to  move  valve  A  towards  the  relay-valve  head  G.  Cylin- 


Fig.  293. — Section  Lombard  Eelay  Valve. 

der  E  is  in  communication  through  pipes  I  and  J  with  the  adjusting- 
valve  14,  and  also  through  the  pipes  J  and  K  with  the  displacement- 
cylinder  107.  The  regulating  valve  14  is  capable,  when  moved 
in  one  direction,  of  admitting  liquid  under  full  pressure  into  the  pipe, 
I,  and,  when  moved  in  the  other  direction,  of  exhausting  liquid 
through  the  pipe  I.  In  the  former  case  the  action  is  to  increase 
the  pressure  back  of  the  piston  C  until  it  overpowers  the  piston  B, 
thereby  moving  valve  A  towards  the  relay-valve  head  F,  simulta- 
neously opening  the  upper  cylinder-port  to  the  main  exhaust,  and 


484  The  Water  Wheel  Governor. 

the  lower  cylinder-port  to  the  main  pressure  supply.  Instantly  the 
main  piston  of  the  governor  and  with  it  the  displacement-plunger 
109  are  set  in  motion. 

"As  the  displacement-plunger  begins  to  move,  a  space  is  created 
back  of  it,  into  which  a  portion  of  the  liquid  flowing  through  the 
pipe  I  is  diverted.  As  the  motion  of  the  displacement-plunger  be- 
comes more  rapid,  a  condition  is  reached  when  all  the  liquid  flowing 
through  I  continues  on  through  K  into  the  displacement-chamber. 
The  relay-valve  A  then  ceases  to  move  any  further.  The  motion 
of  the  main  governor-piston,  however,  continues  as  long  as  the 
regulating-valve  14  is  open.  When  this  valve  14  closes,  the  relay- 
valve  A  is  immediately  thereafter  closed,  because  the  liquid  in  the 
cylinder  E  instantly  escapes  through  the  pipes  J  and  K  into  the 
space  beneath  the  moving  displacement-plunger;  thus  the  whole 
governor  is  brought  to  rest. 

.  "When  the  regulating-valve  14  is  moved  in  the  opposite  direction 
by  the  centrifugal  balls  so  as  to  allow  liquid  to  escape  through  the 
pipe  I,  there  results  an  immediate  loss  of  liquid  in  the  cylinder  E, 
back  of  the  plunger  C ;  this  allows  the  plunger  B  to  force  the  relay- 
valve  A  towards  the  rday-valve  head  G,  thus  opening  the  lower 
cylinder  port  to  the  exhaust,  and  the  upper  cylinder-port  to  the 
pressure  supply.  The  main  governor-piston  instantly  begins  to 
move  down,  carrying  with  it  the  displacement-plunger,  thus  forcing 
liquid  through  the  pipes  K  and  I,  reducing  the  flow  outward  through 
J,  until  finally  the  downward  velocity  of  the  displacement-plunger 
becomes  rapid  enough  to  entirely  check  the  outward  flow  through  J. 
Relay-valve  A  then  remains  stationary  until  the  valve  14  has  moved 
to  a  new  position.  As  soon  as  regulating-valve  14  is  closed,  the  liq- 
uid which  has  been  flowing  out  through  I  immediately  flows  into  J 
and,  acting  upon  the  plunger  C,  restores  valve  A  to  its  closed  posi- 
tion, stopping  further  movement  of  the  governor.  It  will  be  seen 
that  the  governor  when  moving  has  a  constant  tendency  to  close 
the  relay-valve  which  keeps  it  in  motion,  and  this  relay-valve  can 
be  maintained  open  only  so  long  as  the  regulating-valve  14  is  add- 
ing or  subtracting  oil  to  or  from  the  system  consisting  of  the  pipes 
I,  J,  K,  and  parts  connected  therewith." 

Fig.  294  shows  the  Lomard  Governor,  Type  R,  the  smallest  of  the 
various  governors  made  by  that  company.  This  is  a  vertical,  self- 
contained  oil  pressure  machine.  The  oil  is  stored  in  a  tank  formed 
by  the  main  frame.  The  governor  is  designed  to  exert  2500  pounds 


The  Lombard  Governor. 


485 


pressure  and  will  make  an  extreme  stroke  of  eight  inches  in  one 
second. 

239.  Operating  Results  with  Lombard  Governor.— Fig.  295  is 
a  cut   from   a  speed   recorder  strip  taken  from  the  Hudson   River 


Fig.  294.— The  Lombard  Type  R  Governor. 

Power  Transmission  Companies  plant  and  shows  the  regulation  of 
the  Lombard  Type  B  Governor  regulating  S.  Morgan  Smith  tur- 
bines on  an  electric  railroad  load.  The  cars  are  large  and  the 
change  in  load  rapid  and  large. 


486 


The  Water  Wheel  Governor. 


1  ! 


Fig.  296  shows  the  comparative  regula- 
tion of  two  generators  in  the  same  plant. 
(See  Bulletin  No.  107  Lombard  Gov- 
ernor Company.)  The  load  was  quite 
variable  on  account  of  beaters  which  had 
to  be  driven  from  the  same  shaft  as  the 
paper  making  machinery.  The  original 
governor  used,  the  work  of  which  is  shown 
in  the  upper  cut,  was  replaced  by  a  Lom- 
bard Type  D  Governor.  The  work  of 
the  latter  is  shown  in  the  lower  tacho- 
meter chart,  and  the  improvement  in  the 
uniformity  of  operation  is  readily  seen  by 
a  comparison  of  the  twro  charts. 

240.  The  Sturgess  Hydraulic  Gover- 
nor.*— The  Sturgess  Type  "M"  Hydrau- 
lic Governor,  with  the  omission  of  the 
pump  and  storage  tank,  is  shown  in  Fig. 
297  and  in  section  in  Fig.  298.  This  gov- 
ernor consists  of  a  shaft-type  centrifugal 
governor  G  attached  to  the  top  of  the  ma- 
chine and  operated  by  a  belt  and  pulley 
P  from  the  turbine  shaft.  The  governor 
balls  BB  in  this  machine  control  directly  by 
means  of  a  long  vertical  lever  D  a  small 
primary  or  pilot  valve  S  of  cylinder  type 
which  admits  oil  to  a  cylinder  controlling 
the  main  admission  valve  S.  The  main 
valves,  attached  to  the  side  of  the  cylin- 
der, admit  pressure  directly  into  the  cyl- 
inder S  and  on  either  side  of  the  piston*  S 
which,  by  its  motion,  rotates  the  gate 
shaft  by  means  of  the  concealed  steel  rack 
R  and  pinion  N,  shown  in  the  sectional 
view,  Fig.  298. 

The  valves  for  the  admission  of  oil  or 
water,  as  the  case  may  be,  in  the  cylinder 
are  of  the  poppet  type  which  avoid  lap" 
and  therefore  increase  the  sensitiveness  of 
the  governor.  The  anti-racing  mechanism 

*: Sturgess  Engineering  Dept.  of  The  Ludlow 
Valve  Mfg.  Co.,  Troy,"N.  Y. 


Operating  Results  with  Lombard  Governor. 


487 


488 


The  Water  Wheel  Governor. 

G 

P 


B 


Fig.  297.— Sturgess  Type  M  Hydraulic  Governor. 


The  Sturgess  Hydraulic  Governor. 

G 


489 


Fig.  298.— Section  Sturgess  Type  M  Governor. 

consists  of  a  rod  A  which  is  attached  to  the  cross  head  of  the 
governor.  At  the  top  of  this  rod  is  a  projection  to  which 
is  attached  an  adjustable  piston  rod  reaching  down  into  the  open 
top  dash  pot  F.  The  piston  rod  has  a  piston  attached  at  its  lower 
end  fitting  freely  into  the  bore  of  the  dash  pot  the  top  of  which  is 


49° 


The  Water  Wheel  Governor. 


formed  into  a  cup  which  receives  the  excess  oil.  The  bottom  of  the 
dash  pot  is  closed  and  is  attached  to  a  tail, piece  connected  to  the 
counter  weighted  locker  lever,  C. 

The  piston  rod  and  piston  are  hollow  and  near  the  bottom  of  the 
piston  is  a  small  by-pass  which  can  be  regulated  by  an  adjusting 
screw  which  controls  the  rate  of  flow  of  the  oil  in  the  dash  pot.  The 
lever,  C,  is  fixed  on  the  rocker  shaft  the  opposite  end  of  which  car- 
ries the  short  arm  from  which  a  link  is  carried  to  the  bottom  of  the 
valve  lever  D  which  is  free  to  move.  Two  weights,  EE,  are 


Speed 


8.  A  B.  TACHOMETER  No.  10,205 

^Revolution*  pc-r  Miu. 


,„  Revolution*  pi-r  Mln. 


L\\\\\\ 


ffffff 


,  \  0 

\T\T\  \\\\\\\  U  \\  \\.\\\\ 


'.  3 


1 

11 

''i 

L 

"- 

1 

1 

Movements  of      , 

^ 

A 

ll 

! 

J 

In 

f 

tr 

j 

•£; 

ui 

jvcraor  and  Gate'5 

ut 

U 

,i  j.,, 

n| 

i.'i-t 

.2 

+ 

Closed 

(/ 

I 

V, 

rr 

Fig.  299.— Test  Kesults  with  Sturgess  Governor. 

hung  loosely  on  the  rocker  shaft  but  a  pin  on  the  shaft  engages  with 
either  one  or  the  other  of  the  weights  and  raises  them  whenever  the 
rocker  shaft  moves.  The  function  of  the  weights  therefore  is  to 
keep  the  rocker  shaft,  and  consequently  the  bottom  of  the  valve 
lever,  in  normal  position.  When  the  main  piston  moves,  it  is  ob- 
vious that  it  will  tend  to  raise  or  lower  the  dash  pot,  F,  through 
its  connection  to  the  ro^d  I  and  this  movement  will  swing  the  lever 
C  and  rocker  shaft  H  thus  deflecting  the  bottom  of  the  valve  lever 
D  so  as  to  compensate  in  the  correct  manner.  The  same  movement 
raises  one  of  the  weights  E,  but  as  the  dash  pot  permits  a  slow 
movement  the  weights  will  finally  restore  all  parts  to  the  middle  or 


Test  Results  with  Sturgess  Governor.  491 

normal  position.  In  the  smaller  sizes  the  pilot  valve  is  omitted 
and  the  centrifugal  governor  balls  actuate  directly  through  the 
lever  the  main  valves  of  the  system. 

241.  Test  Results  with  Sturgess  Governor. — The  action  of  any 
governor  in  maintaining  a  uniform  speed  may  be  shown  graphi- 
cally by  attaching  a  recording  tachometer  to  the  turbine  shaft.    In 
order  to  fully  understand  and  appreciate  the  action  of  the  governor, 
the  tachometer  chart  should  be  considered  together  with  the  load 
curve  and  a  diagram  showing  the  movement  of  the  governor  dur- 
ing the  same  period. 

Fig.  299  shows  a  governor  test  made  by  Mr.  John  Sturgess  on  an 
1 100  K.  W.  unit.  "The  curves  were  traced  by  a  sp.ecial  Schafer  & 
Budenberg  tachometer,  the  readings  being  sufficiently  magnified  to 
bring  out  the  characteristics  of  the  governor.  *  *  *  The  load 
changes  and  governor  movements  are  platted  below.  Note  that  when 
the  whole  load  was  thrown  off  (at  1 :55),  the  speed  accelerated  about 
8  per  cent,  in  an  incredibly  short  time  (under  i  sec.),  and  the  gov- 
ernor had  the  gate  shut  in  14  sees,  after  the  load  went  off.  *  *  * 
It  is  to  be  noted  that  after  the  first  quick  result  at  2  :oo  mins.  the 
governor  slowly  oscillated  for  about  another  minute,  but  with 
gradually  increasing  gate  opening,  the  speed  and  load  being  prac- 
tically constant.  This  was  due  to  the  water  rising  in  the  forebay, 
and  gradually  subsiding  in  a  succession  of  waves,  the  governor  tak- 
ing care  of  these  fluctuations,  in  effective  head,  in  a  very  intelligent 
manner."* 

"The  plant  in  which  these  tests  were  made  was  by  no  means  a 
good  one  from  the  regulation  standpoint,  for  it  will  be  noticed  that 
when  the  whole  load  was  instantly  thrown  off  the  momentary  rise 
of  speed  was  about  8  per  cent,  although  the  governor  shut  the 
gate  from  full  open  position  in  the  extremely  quick  time  of  1.4 
sees.  There  were  five  wicket  gates,  having  a  total  of  96  leaves,  and 
a  heavy  counter-weight  to  be  moved  a  considerable  distance  in  this 
interval.  ** 

242.  General  Consideration.— Mechanical  governors  are  cheaper 
than  hydraulic,  but,  assuming  the  same  gate  movement,  they  are 
less  effective  at  increasing  loads  since  the  power  to  move  the  gates 
must  be  taken  as  needed  from  the  wheel  itself  instead  of  being  taken 

*  See  American  Society  M.  E.,  Vol.  27,  No.  4,  p.  8. 

**  Catalogue  of  Water  Wheel  Governors,  Sturgess  Engineering  Department 
of  the  Ludlow  Valve  Co.,  p.  23. 


492 


The  Water  Wheel  Governor. 


from  a  storage  tank  as  with  hydaulic  governors.  This  is  a  factor 
of  more  or  less  importance  in  accordance  with  the  degree  of  regu- 
lation required.  The  difference  is  manifest  principally  at  low  loads 
when  the  energy  taken  by  the  governor  relay  from  the  water  wheel 
is  a  considerable  percentage  of  the  total  energy  being  generated.  As 
the  power  exerted  by  the  relay  is  usually  comparatively  small,  the 
difference  in  action  from  this  cause  between  the  two  types  of  gov- 
ernors is  often  unimportant- 


^4  i 


Fig.  300. — Governor  Connection  by  Diaw  Rods. 

The  hydraulic  governor  possesses  an  additional  advantage  in  its 
ability  to  start  a  stationary  wheel  into  action  by  means  of  its 
stored  energy.  The  mechanical  governor  depending  as  it  does  on 
the  power  of  the  wheel  itself  is  only  effective  after  the  wheel  has 
been  started  by  other  means. 

243.  Control  From  the  Switchboard. — Electrical  devices  can  now 
be  purchased  by  which  the  normal  speed  of  the  wheels  can  be  con- 
trolled from  the  switchboard  in  case  the  governor  is  so  designed 
that  it  can  be  adjusted  while  in  motion,  which  is  true  of  most  high 
class  machines.  It  is  also  possible  to  start  and  stop  the  wheels 
electrically  from  the  switchboard  or  from  a  distant  station. 


Connection  of  Governors  to  Gates.  493 

244.  Connecton  of  Governors  to  Gates. — The  following  discussion 
of  this  subject  and  the  accompanying  figures  are  taken  with  slight 
changes,  from  a  paper  by  Mr.  A.  V.  Garratt.* 

«  *  *  *  rpke  most  successful  method  of  connecting  the  cylinder 
gates  of  several  turbines  to  the  same  governor  is  shown  in  Fig.  300. 
In  this  case  each  pair  of  drawrods  is  connected  to  a  pair  of  walking 
beams  which  carry  counterweights  on  their  opposite  ends.  Each 
walking  beam  carries  a  gear  sector  which  engages  a  rack  on  a  long, 
horizontal  reciprocating  member  terminating  at  the  governor. 
The  racks  on  the  reciprocating  member  are  "sleeved"  on  it,  and  held 
in  place  by  pins,  which  may  be  removed  if  it  is  desired  to  discon- 
nect any  turbine  from  the  governor. 

"By  this  method  any  one,  or  any  combination  of  turbines,  may  be 
handled  by  the  governor  or  any  turbines  by  hand,  at  will,  by  means 
of  a  lever  shown  in  the  end  projection. 

"Fig.  301  shows  a  good  method  of  connecting  a  governor  to  a 
pair  of  horizontal  wicket-gate  turbines.  It  will  be  noted  that  the 
shaft  connecting  the  two  gear  sectors  on  the  gate  stems  goes  di- 
rectly to  the  governor,  and  is  connected  to  it  through  a  pin  clutch 
which  may  be  opened,  and  a  hand-wheel  on  the  governor  may  then 
be  used  to  move  the  gates  by  hand.  The  only  improvement  on 
this  design  which  can  be  suggested  would  be  to  eliminate  the  coun- 
ter-shaft between  the  governor  pulleys  and  the  turbine  shaft  by  plac- 
ing the  governor  beyond  the  draught-tube  quarter-turn,  so  that 
the  governor  pulleys  might  belt  directly  to  the  turbine  shaft.  The 
limitations  of  available  space  prevented  the  location  of  the  governor 
in  this  manner  on  the  drawing  which  shows  the  design  used  for 
three  units  in  a  modern  power  plant. 

"Frequently  the  only  possible  location  of  the  governor  prevents 
anything  like  direct  connection  between  it  and  the  turbines.  In 
such  cases  experience  has  shown  that  it  is  wisest  to  avoid  the  use 
of  several  pairs  of  bevel  gears  and  long  shafts,  and  in  their  place 
nse  a  steel  rope  drive.  This  method  has  great  flexibility,  and  per- 
mits of  governor  locations  which  would  otherwise  be  impossible. 
Fig.  302  shows  a  design  of  this  kind.  The  governor  is  located  in 
the  only  available  space,  and  yet  its  connection  to  the  turbines  is 
perfectly  adequate.  The  steel  rope  used  is  small  in  size,  made  of 
very  small  wire,  especially  laid  up,  and  its  ends  are  fixed  to  the 
grooved  sheaves,  which  are  provided  with  internal  take-ups,  so 

*  See  "Speed  Regulation  of  Water  Power  Plants,"  by  Allan  V.  Garratt.  Cas- 
sier's  Magazine,  May,  19'01. 

30 


494 


The  Water  Wheel  Governor. 


nnn 


Fig.  301. — Governor  Connection  by  Shaft  and  Sectors. 


Relief  Valves. 


495 


that  the  rope  may  be  kept  tight  as  a  fiddle  string.  This  general 
method  of  connection  is  in  successful  use  in  many  plants  where 
the  requirements  for  speed  regulation  are  most  exacting. 

"In  the  above  examples  the  two  ends  which  have  governed  the 
design  are  simplicity  and  directness.  These  two  factors  should 
never  be  lost  sight  of,  and  the  more  completely  they  are  embodied 
in  the  design,  the  better  will  be  the  speed  regulation.  To  these  two 
may  be  added  another,  and  that  is  freedom  from  lost  motion.  These 


Fig.  302. — Governor  Connection  by  Cable. 

three  factors  are  absolutely  necessary  if  successful  results  are  to  be 
expected.  The  slightest  motion  of  the  governor  must  be  trans- 
mitted in  the  simplest  and  most  direct  manner,  and  in  the  shortest 
possible  interval  of  time,  to  the  turbine  gates/' 

245.  Relief  Valves. — Relief  valves  are  very  necessary  on  long 
feeder  pipes  and  penstocks  to  avoid  excess  pressures  of  an  acci- 
dental nature  as  well  as  those  produced  by  closing  of  the  turbine 
gates.  A  group  of  such  valves  installed  on  the  end  of  one  of  the 
penstocks  of  the  Niagara  Falls  Hydraulic  Power  and  Manufactur- 
ing Co.  is  shown  in 'Fig.  303.  Relief  valves  should  be  arranged  to 
open  with  a  slight  excess  of  the  penstock  pressure  but  should  close 
very  slowly  in  order  to  avoid  oscillatory  waves.  Spring  balanced 


496 


The  Water  Wheel  Governor. 


relief  valves  have  proven  objectionable  for  this  purpose.  If  set 
to  open  at  a  small  excess  pressure  they  are  apt  not  to  close  on  ac- 
count of  the  impact  of  the  discharging  water  against  the  valve, 
In  order  that  they  may  close,  the  balancing  spring  must  be  so  strong 
that  a  considerable  excess  is  required  to  open  the  valve  which  does 
not  therefore  serve  the  desired  purpose.  All  types  of -valves  are 
also  hindered  by  the  fact  that  corrosion  is  apt  to  seal  the  valve  so 
that  a  considerable  excess  is  required  to  open  it. 

246.  Lombard    Hydraulic    Relief    Valve. — The    Lombard    Gov- 


Fig.  303.— Relief  Valve  on  end  of  Penstock.      Niagara  Falls  Hydraulic  Power 
Manufacturing  Co.     (Electrical  World,  Jan.  14,  1899.) 

ernor  Company  have  designed  a  valve  in  which  they  claim  to  have 
eliminated  the  difficulties  of  the  spring  valve.  This  valve  is  shown 
in  Fig.  304*  and  is  described  as  follows : 

"The  valve  consists  of  the  following  parts,  viz : — A  valve  disc,  c, 
capable  of  motion  to  or  from  its  seat,  b,  rigidly  connected  by  means 
of  a  rod,  i,  with  the  piston,  f,  in  the  cylinder,  e.  The  whole  valve  is 
bolted  to  a  flange  upon  the  supply  pipe,  d,  wherein  the  pressure  is 
to  be  controlled.  The  area  oi  piston,  f,  is  somewhat  greater  than 
that  of  the  valve  disc,  c,  so  that  when  water  at  the  same  pressure 
is  behind  the  piston  and  in  front  of  the  valve  there  is  a  positive  and 
strong  tendency  to  hold  the  valve  closed.  For  the  purpose  of  al- 

*  Lombard  Bulletin  No.  101. 


Lombard  Hydraulic  Relief  Valve. 


497 


lowing  the  valve  disc,  c,  to  open  at  proper  times  to  relieve  excess 
pressure  in  the  supply  pipe,  d,  there  is  provided  a  regulating  waste 
valve,  C.  This  valve  is  opened  or  closed  by  a  piston,  n,  opposed 
by  a  very  oblong  and  strong  spiral  spring,  p.  Piston,  n,  is  a  loose 
fit  in  its  cylinder,  o,  so  that  it  moves  upward  freely  in  response 


Fig.  304.— Lombard  Hydraulic  Relief  Valve. 

to  the  least  excess  in  pressure  upward  due  to  the  water  in  the  cylin- 
der, o,  opposed  to  the  downward  pressure  of  the  spring,  p.  *  *  * 
The  piston,  n,  is  connected  by  means  of  the  stem,  m,  with  a  double- 
seated  balanced  valve,  d,  which  of  course,  opens  simultaneously 
with  any  upward  movement  of  the  piston.  Water  under  existing 
pressure  is  admitted  into  the  cylinder,  e,  through  the  pipe,  k,  and 
throttle  valve,  i. 


498  The  Water  Wheel  Governor. 

"The  spring,  p,  is  adjusted  by  means  of  the  screw,  s,  and  lock-nut, 
y,  so  that  the  effective  normal  pressure  of  the  water  in  the  chamber 
is  just  insufficient  to  overcome  the  downward  pressure  of  the 
spring.  The  valve,  D,  will  therefore  remain  closed  normally ;  con- 
sequently the  main  valve  disc,  c,  will  also  remain  closed  normally, 
because  water  flowing  in  through  the  pipe,  k,  and  throttle  valve,  I, 
will  produce  an  excess  closing  pressure  upon  the  piston,  f.  When 
thus  adjusted  any  increase  in  pressure  above  the  normal  will 
immediately  force  the  piston,  n,  upward,  and  will  thereby  open 
the  balanced  valve,  D.  This  instantly  relieves  the  pressure  back 
of  the  piston,  f,  which  of  course  then  gives  way  to  the  superior  pres- 
sure back  of  the  piston,  f,  which  of  course  then  gives  way  to  the 
superior  pressure  in  front  of  valve,  c.  In  this  manner  practically 
the  whole  pressure  in  front  of  the  valve  disc,  c,  is  available  for 
opening  it.  *  *  *  Valve  disc,  c,  will  continue  to  open  until 
the  limit  of  its  travel  has  been  reached,  or  the  pressure  in 
the  supply  pipe,  d,  has  been  reduced  to  a  point  where  the 
piston,  n,  will  close  the  balanced  valve,  D.  Immediately  on  the 
closing  of  balanced  valve,  D,  water  begins  to  accumulate  behind 
the  piston,  f,  flowing  in  through  the  throttle  valve,  I.  This  water 
gradually  and  surely  forces  the  valve  disc,  c,  to  close.  The  speed  of 
closing  is  adjustable  by  the  opening  through  the  throttle  valve,  i, 
and  may  be  made  as  slow  as  several  seconds  or  even  minutes.  The 
closing  motion  is  *  *  uniform  and  there  is  not  the  slightest  ten- 
dency to  set  up  vibrations  in  the  water  column,  a  very  serious  ob- 
jection to  the  ordinary  types  of  spring  balanced  valves  which  open 
and  close  suddenly  and  are  liable  in  the  latter  operation  to  set  up 
water  hammer  effects  even  more  dangerous  than  those  which  they 
are  designed  to  relieve." 

247.  Sturgess  Relief  Valves. — The  Sturgess  Engineering  De- 
partment of  the  Ludlow  Valve  Manufacturing  Company  makes  two 
forms  or  relief  valves,  the  "Automatic"  and  the  "Mechanical." 
The  Automatic  Relief  Valve  is  shown  in  Fig.  305  and  is  described 
as  follows: 

"The  essential  element  in  the  Automatic  Relief  Valves  is  a  large, 
very  sensitive  diaphragm  o.f  special  construction.  This  is  under 
the  influence  of  the  water  pressure  in  the  pipe-line  and  its  move- 
ments are  communicated  to  a  small  pilot  valve  controlling  a  hy- 
draulic cylinder,  which  in  turn  operates  the  relieving  valve  on  the 
relief  valve  proper.  After  the  pressure  in  the  pipe-line  is  restored  to 
normal,  the  relief  valve  gradually  closes  automatically. 


Sturgess  Relief  Valve. 


499 


"The  action  of  this  valve  is  almost  instantaneous,  and  it  will 
iully  open  on  a  very  small  rise  of  pressure. 

"These  valves  can  either  be  made  in  self-contained  form,  or 
the  sensitive  parts  (diaphragm,  pilot  valve,  and  hydraulic  cylin- 


Fig.  305. — Sturgess  Belief  Valve. 

der)   may  be  mounted  on  a  pedestal  placed  in  the  power  house, 
and  the  relief  valve  proper  attached  to  the  penstock  or  wheel  cas- 
ing, a  rod  or  link  being  provided  to  connect  the  two  (as  in  Fig. 
305). 
NOTE. — See  Appendix  for  descriptions  of  two  new  governors. 


CHAPTER  XX. 

ARRANGEMENT  OF  THE  REACTION  WHEEL. 

248.  General  Conditions. — The  reaction  turbine  may  be  set  or  ar- 
ranged for  service  in  a  water  power  plant  in  a  variety  of  ways,  and 
the  best  way  may  differ  more  or  less  with  each  installation.  The 
arrangement  of  wheels  should  always  be  made  with  due  regard  to 
machinery  to  be  operated,  the  local  conditions  that  prevail,  and  es- 
pecial consideration  should  be  given  to  securing  the  greatest 
economy  in  the  first  cost  of  installation,  maximum  efficiency  and 
facility  in  operation,  and  minimum  cost  of  operation  and  mainte- 
nance. 

Impulse  water  wheels  of  the  tangential  type  have  always  been 
set  with  their  shafts  horizontal.  An  installation  with  vertical  shaft 
was  proposed  for  one  of  the  first  Niagara  plants  but  was  not  con- 
sidered on  account  of  the  lack  of  actual  experience  with  such  a 
form  of  installation.  Impulse  wheels  of  the  Girard  type  have  been 
used  with  both  vertical  and  horizontal  shafts.  In  general,  how- 
ever, because  of  the  high  heads  under  which  impulse  wheels  usually 
operate,  the  horizontal  shaft  arrangement  is  readily  adapted. 
When  an  impulse  wheel  is  installed  it  must  be  set  above  the  level 
of  maximum  tail  water,  if  it  is  to  be  operated  at  all  stages  of  water. 
The  wheel  arrangement  is  therefore  dependent  principally  on  the 
arrangement  of  the  machinery  to  be  operated.  By  far  the  greater 
proportion  of  such  machinery  is  built  with  horizontal  shafts  and 
hence  in  most  cases  where  machinery  is  not  special,  horizontal 
shaft  arrangements  are  desirable. 

Reaction  wheels  are  often  used  on  streams  where  the  relative 
variation  in  position  of  the  tail-water  is  considerable,  and  it  is  both 
desirable  to  utilize  the  full  head  and  to  have  the  wheel  set  at  an  ele- 
vation at  least  above  the  lowest  elevation  of  the  tail-water  in  order 
that  they  may  be  accessible  for  examination  and  repairs.  By  the 
use  of  the  draft  tube  this  can  often  be  done  without  the  sacrifice 
of  head.  If  the  wheel  must  be  set  below  tail-water,  gates  must  be 
provided  for  the  tail-race  with  pumps  for  the  removal  of  the  water 
when  access  to  the  wheels  is  necessarv. 


Necessary  Submergence  of  Reaction  Wheels.  501 

The  arrangement  of  reaction  water  wheels  is  susceptible  only  of 
general  classification,  which,  however,  may  assist  in  the  under- 
standing of  the  subject  and  the  selection  of  the  best  methods  to  be 
adopted  under  any  set  of  local  conditions.  Wheels  may  be  set 
vertically  or  horizontally,  as  the  conditions  of  operation  demand, 
without  materially  affecting  their  efficiency,  provided  that  in  each 
instance  the  turbine  case,  draft  tubes,  etc.,  are  suitably  arranged. 
The  improper  design  of  the  setting  may  materially  affect  the  effi- 
ciency of  operation  in  either  case. 

249.  Necessary  Submergence  of  Reaction  Wheels. — In  order  to 
prevent  the  formation  of  a  vortex  or  whirlpool,  which  will  draw 
air  into  the  wheel  and  often  seriously  affect  its  power  and  efficiency, 
it  is  necessary  that  the  gate  openings  of  the  wheel  be  placed  from 
one   to   one   and    one-quarter   wheel    diameters   below   the    water 
surface.    The  head  under  which  the  wheel  is  to  operate,  however, 
greatly  affects  the  formation  of  the  vortex.    High  velocities  of  flow 
will  facilitate  their  formation,;  therefore  greater  heads  will  require 
a  greater  water  covering  or  other  means  for  the   prevention  of 
vortex  formation. 

As  the  wheel  usually  has  a  greater  diameter  than  the  height  of 
the  gate  it  can  be  set  vertically  with  less  danger  of  air  inter- 
ference than  when  set  horizontally.  For  this  reason  the  vertical 
wheels  are  more  readily  adapted  to  low  heads  and  have  in  the  past 
been  more  widely  used  for  developments  under  low  and  moderate 
heads. 

With  both  horizontal  and  vertical  wheels  the  wheel  may  be  pro- 
tected from  the  formation  of  the  vortex  by  a  solid  wooden  float,  or 
may  be  partially  encased  or  covered  with  an  umbrella-shaped  cover 
the  edges  of  which  can  be  brought  below  the  level  of  the  upper 
gates  of  the  turbine  thus  allowing  the  wheel  to  be  set  near  the 
head  water  surface  without  the  serious  interference  above  men- 
tioned. In  all  such  cases  the  float  or  cover  must  be  so  arranged  as 
to  admit  the  water  to  the  wheel  gates  without  undue  velocity  in 
order  to  prevent  the  loss  of  head.  If  this  is  done  the  efficiency  and 
power  of  the  wheel  will  not  be  affected  (see  Appendix  E).  Arrange- 
ments of  this  sort  were  designed  by  the  writer,  in  the  fall  of 
1906,  for  the  water  power  plants  at  Kilbourn  and  at  Dresden 
Heights. 

250.  Arrangements  of  Vertical   Shaft  Turbines. — Figs.  306  and 
307  show  twelve  typical  arrangements  of  reaction  turbines.    Figs. 
A,  B,  C  and  D  of  Fig.  306  show  typical  arrangements  of  vertical 


502 


Arrangement  of  the  Reaction  Wheel. 


A 


Fig.  306. 


Arrangement  of  Vertical  Shaft  Turbine.  503 

wheels.  Diagram  A  is  the  most  common  arrangement  of  the  re- 
action turbine  in  an  open  penstock  for  low  head.  In  this  case  the 
wheel  is  set  in  a  chamber  called  the  wheel  pit,  the  flume,  or  some- 
times the  penstock,  and  is  connected  with  the  head  race  from  which 
it  should  be  separated  by  gates.  The  wheel  pits  in  the  smaller 
plants  have  commonly  been  constructed  of  timber;  but  in  the  larger 
plant,  they  are  usually  built  of  a  more  substantial  character, — 
often  of  iron  or  concrete,  usually  reinforced.  Sometimes  two  or 
more  wheels  are  set  in  a  single  pit ;  but  in  the  better  class  of  con- 
struction, a  pit  is  supplied  for  each  individual  wheel  or  each  unit 
combination  of  wheels  so  that  each  unit  can  be  cut  off  from  its 
fellows,  disconnected  from  the  transmission  mechanism  to  which 
it  is  attached,  and  examined  or  repaired  without  interference  with 
the  remainder  of  the  plant.  Open  pits  are  commonly  used  for 
heads  up  to  18  or  20  feet  and  may  be  used  for  considerably  higher 
heads  under  favorable  conditions. 

For  higher  heads,  the  arrangement  shown  in  diagram  B,  or  some 
other  form  similar  thereto,  is  often  found  more  desirable.  In  this 
case  closed  flumes  of  steel  or  reinforced  concrete  are  used,  and  are 
connected  with  the  head  race  by  metal,  wood,  or  reinforced  con- 
crete pipes  to  which  the  term  "penstock"  is  commonly  applied. 
This  form  of  construction  permits  of  the  use  of  vertical  wheels 
with  almost  any  head.  In  Diagram  B  the  turbine  is  shown  as  di- 
rect connected  to  an  electrical  generator  of  special  design  with  ver- 
tical shaft. 

In  Diagram  A  the  shaft  of  the  turbine  is  shown  as  directly  at- 
tached to  a  crown  gear  which  in  turn  is  connected  by  a  spur  gear 
with  a  horizontal  shaft.  This  horizontal  shaft  may  be  direct-con- 
nected to  a  generator  as  shown  in  Fig.  325,  or  may  be  attached  by 
belting,  ropes,  cable  or  other  mechanical  means  with  one  or  more 
machines  which  it  is  designed  to  operate. 

Diagrams  C  and  D  show  two  vertical  types  of  settings  of  tan- 
dem or  multiple  wheels.  Such  arrangements  are  introduced  when 
it  is  necessary  to  reduce  the  diameter  of  the  wheels  on  account  of  in- 
creased speed,  and  at  the  same  time  maintain  the  power  of  in- 
stallation by  increasing  the  number  of  wheels  for  the  purpose  of 
direct  connection  to  some  machine  to  be  operated  . 

In  all  cases  where  two  wheels  discharge  into  a  common  draft 
tube  sufficient  space  is  necessary  between  the  wheels  to  prevent 
interference  and  consequent  loss  in  efficiency.  The  arrangement 


504  Arrangement  of  the  Reaction  Wheel. 

of  wheels  in  this  manner  therefore  requires  a  considerable  amount 
of  vertical  space  and,  under  low  or  moderate  head,  involves  the 
construction  of  a  wheel  pit  of  considerable  depth  in  order  to  se- 
cure proper  submergence  of  the  upper  wheel.  This  arrangement 
results  in  the  lower  wheel  being  often  considerably  below  the  tail- 
water  and  necessitates  the  use  of  tail  gates  and  a  pumping  plant 
to  remove  the  water  in  order  to  make  the  lower  wheels  accessible. 
With  this  design  the  plant  is  made  comparatively  narrow  but  the 
greater  depth  of  construction  means  an  additional  expense  in  the 
foundation  work.  Vertical  wheels  of  all  types  involve  a  design 
of  satisfactory  vertical  bearings  which  are  usually  less  accessible 
than  in  the  case  of  horizontal  bearings  which  can  be  placed  at  an 
elevation  above  the  power  house  floor,  and  are  consequently  more 
readily  accessible.  The  st$p  bearings  for  single  vertical  wheels 
have  been  long  in  use  and  are  reasonably  satisfactory.  The  sus- 
pension bearing,  which  is  involved  in  the  use  of  large  vertical  in- 
stallations, is  not  universally  satisfactory  and,  in  fact,  considerable 
difficulties  have  been  encountered  in  so  designing  a  bearing  that  it 
will  operate  without  undue  expense  for  maintenance. 

251.  Arrangement  of  Horizontal  Turbines. — Single  horizontal 
wheels  of  the  common  type  are  shown  in  Diagrams  E  and  F  of  Fig. 
306  and  in  Diagrams  A,  B,  C,  and  D  of  Fig.  307.  In  each  case  the 
gates  of  the  turbine  must  be  readily  accessible  to  the  entering 
water  without  undue  velocity,  and  the  wheel  pit,  or  penstock,  must 
be  designed  with  this  requirement  in  view. 

Diagrams  E  and  F,  Fig.  306,  and  A,  Fig.  307,  show  horizontal 
types  of  wheels  set  in  an  open  wheel  pit  or  penstock. 

In  Diagram  E  the  wheel  has  the  quarter  turn  set  entirely  in  the 
pit,  and  the  main  shaft  passes  through  a  bulkhead  in  the  wall  of 
the  station  with  a  packing  gland  to  prevent  the  passage  of  water. 
In  this  case  the  water  must  flow  by  the  quarter-bend  and  hence, 
in  order  to  secure  sufficiently  slow  velocity,  the  wheel  pit  must  be 
wider  or  deeper  than  in  the  case  shown  in  Diagram  F  of  Fig.  i. 
Here  the  gates  of  the  turbine  are  placed  toward  the  entering  water 
and  the  flow  is  interfered  with  only  by  the  pedestal  bearings  which, 
being  placed  in  the  center  of  the  crown  or  cover  plate  of  the  wheel, 
occupy  but  little  space  and  offer  practically  no  obstruction  to  flow. 

Diagram  A  of  Fig.  307  is  essentially  the  same  in  arrangement 
as  Diagram  F  in  Fig.  306,  except  that  in  this  case  instead  of  a  me- 
tallic quarter-turn  and  draft-tube,  the  quarter-turn  and  draft-tube 
are  constructed  in  the  masonry  of  the  power  station  and  the  bulk- 


Arrangement  of  Horizontal  Shaft  Turbine.  505 


Fig.  307. 


506  Arrangement  of  the  Reaction  Wheel. 

head  is  reduced  to  simply  a  packing  gland  through  which  the  shaft 
•enters  the  power  station. 

Diagrams  B,  C,  and  D,  Fig.  307,  illustrate  three  methods  of  en- 
closing a  turbine  in  a  closed  flume  which  is  connected  with  the 
head  water  by  a  closed  penstock. 

In  Diagram  B  the  turbine  case  is  spiral,  the  water  enters  tangent 
to  the  wheel  and  at  right  angles  to  the  shaft  and  is  discharged 
through  a  metal  quarter-bend  into  a  concrete  draft-tube. 

In  Diagram  C  the  water  enters  the  metallic  flume  in  which  the 
wheel  is  placed  at  right  angles  to  the  shaft,  and  is  discharged 
through  a  metal  quarterrbend  and  draft-tube. 

In  Diagram  D  the  water  enters  the  wheel  case  parallel  to  the 
shaft  of  the  wheel  and  is  discharged  through  a  metal  quarter-bend 
into  a  concrete  draft-tube. 

Figs.  E  and  F  of  Fig.  307  show  methods  of  setting  horizontal 
shaft  wheels  in  tandem.  Diagram  F  is  for  setting  in  an  open 
flume  or  penstock.  The  two  wheels  discharge  into  a  common 
shaft  chest  and  use  a  common  draft-tube.  In  Diagram  E  the  wheels 
have  a  common  closed  case  or  flume  connected  by  a  penstock  with 
the  head  waters  and  each  discharges  through  an  independent  quar- 
ter-turn and  an  independent  draft-tube  into  the  tail-waters  beneath. 
With  the  closed  flume  removed,  this  arrangement  can  also  be  used 
in  an  open  penstock.  These  diagrams  are  simply  typical  of  various 
possible  arrangements  of  wheels  that  can  be  adapted  with  various 
modifications  of  detail  to  meet  the  local  requirements  of  the  en- 
gineer for  any  hydraulic  plant  which  he  may  be  called  upon  to  de- 
sign. 

252.  Classification  of  Wheels.— The  classification  of  the  arrange- 
ment of  wheels  as  shown  in  Figs.  306  and  307  may  be  reviewed 
briefly  as  follows : 

In  this  review  reference  is  given  to  various  figures  in  the  pre- 
ceding and  following  text  in  which  the  type  of  wheel  described  is 
illustrated  with  more  or  less  modifications. 

ist.  Vertical  single  wheel,  open  wheel  pit.  (See  Diagram  A, 
Fig.  306,  also  Figs.  329,  331,  333  and  334.) 

2nd.  Vertical  single  or  tandem  wheels  in  metal  casing  con- 
nected by  cylindrical  penstock  with  supply.  (See  Diagram  B,  Fig. 
306,  also  Figs.  132,  181,  310,  311.) 

3rd.  Vertical  tandem  wheels, — two  or  more  wheels  in  open  pit. 
(See  Diagrams  C  and  D,  Fig.  306,  also  Figs.  134,  138,  173,  339.) 


Classification  of  Wheels.  507 

4th.  Horizontal  turbine,  open  wheel  pit,  quarter-bend  and  draft- 
tube  within  wheel  pit, — quarter  bend  of  metal.  (See  Diagram  E, 
Fig.  306.) 

5th.  Horizontal  turbine,  open  wheel  pit,  quarter-bend,  and  draft- 
tube  exterior  to  pit, — quarter-bend  may  be  of  metal  or  concrete 
construction.  (See  Diagram  F,  Fig.  306,  also  Diagram  A,  Fig. 
307  and  Figs.  314,  322.) 

6th.  Horizontal  turbine  in  spiral  case  at  end  of  penstock,  single 
or  double  draft-tube.  (See  Diagram  B,  Fig.  307,  also  Figs.  159, 
162,  338.) 

7th.  Horizontal  turbine  in  cylindrical  or  conical  case  at  end  of 
penstock.  (See  Diagrams  C  and  D,  Fig.  307,  also  Fig.  335.) 

8th.  Tandem  horizontal  turbines  in  open  wheel  pit,  single  dis- 
charge through  common  or  independent  draft  tubes.  (See  Diagram 
F.  Fig.  307,  also  Figs.  315,  319  to  324  inclusive.) 

9th.  Tandem  horizontal  turbine  in  enclosed  cylindrical  case  with 
common  penstock  and  common  or  independent  draft-tubes.  (See 
Diagram  E,  Fig.  307,  also  Figs.  13,  140,  152,  317.) 

253.  Vertical  Wheels  and  Their  Connection. — The  vertical  set- 
ting of  single  wheels  is  usually  the  cheapest  in  first  cost,  which 
fact  is  an  important  factor  that  has  been  largely  instrumental  in 
the  adoption  of  this  arrangement  in  most  of  the  older  plants.    Ver- 
tical wheels  are  most  commonly  set  in  open  wheel  pits.    They  may, 
however,  be  set  in  a  cast  iron  or  steel  casing  which  is  then  con- 
nected to  the  headrace  or  dam  by  a  proper  penstock.     Single  ver- 
tical wheels  can  be  connected  to  the  machine  they  are  to  drive  by 
various  means.    Belting,  transmission  ropes,  cables,  and  shaftings, 
are  in  common  use  for  such  connections.  The  shaft  is  usually  placed 
horizontally  and  is  connected  by  a  crown  beveled  gear  and  pinion 
to  the  wheel.    Frequently  belts,  ropes,  and  cables  are  connected  by 
pulleys  or  sheaves  to  a  short  horizontal  shaft  driven  in  the  same 
manner.    When  the  power  of  a  single  vertical  wheel  is  insufficient, 
two  or  more  may  be  harnessed  by  gearing  to  a  line  shaft  which  may 
be  directly  connected  to  the  machine  or  machines  to  be  operated, 
or  otherwise  connected  as  convenience  and  conditions  may  require. 

254.  Some  Installations  of  Vertical  Water  Wheels. — Figs.  329  to 
332  inclusive,  show  the  plans,  elevations,  sections,  and  details  of 
a  small  plant  of  vertical  water  wheels  designed  by  the  writer  for 
the  Sterling  Gas,  Light  and  Power  Company  of  Sterling,  Illinois. 
The  details  of  this  plant  are  clearly  shown  by  the  illustrations  and 
will  be  discussed  at  some  length  later.    This  plant  is  located  on  the 


5o8 


Arrangement  of  the  Reaction  Wheel. 


oo 
o 

CO 

to 


Some  Installations  of  Vertical  Water  Wheels. 


5o9 


Sterling  side  of  the  Rock  River  (See  Fig.  345)  and  is  next  to  the 
last  plant  on  the  Sterling  Race.  The  head  developed  is  about  eight 
feet  and  the  power  of  each  wheel  is  about  115  h.  p.  under  this  head. 
Each  wheel  of  the  installation  is  set  in  an  independent  pit -or  pen- 
stock which  can  be  closed  by  means  of  a  flume  gate.  The  wheels 
are  connected  to  a  common  shaft  extending  into  the  power  house 
and  connected  with  pulleys  and  belts  to  the  generator. 

The  plan  of  the  South  Bend  Electric  Company  at  Buchanan, 
Michigan,  is  of  similar  type  and  is  shown  on  page  544,  Fig.  334.  The 
main  shaft  is  here  connected  with  ten  turbines  and  is  in  turn 
directlv  connected  to  an  electric  alternator. 


Fig.  309.— Low  Head  French  Water  Power  Plant. 


The  adaptability  of  the  vertical  shaft  turbine  to  low  head  is  well 
shown  in  Figs.  308  and  309.  Fig.  308  shows  three  turbines  manufac- 
tured by  The  Trump  Manufactnring  Company  of  Springfield,  Ohio. 
These  turbines  are  61,  56  and  44"  respectively,  and  by  suitable  gear- 
ings are  connected  with  a  common  shaft.  These  wheels  were  in- 
stalled at  Bologna,  Italy,  and  operate  under  a  low  water  head  of  42" 
and  under  a  high  water  head  of  28".  It  was  necessary  to  set  the 
wheels  considerably  below  the  level  of  the  tail  water  in  order  that 
31 


Arrangement  of  the  Reaction  Wheel. 


the  turbines  should  have  a  sufficient  submergence  for  operation. 
Fig.  309  is  a  similar  plant  installed  at  Loches,  France.  In  this 
case  the  water  is  conducted  to  the  turbines  by  means  of  a  syphon 
supply  pipe  in  order  that  the  turbine  might  be  placed  high  enough 
above  tail-water  that  it  be  accessible  at  all  times  without  the 
__  use  of  a  tail-gate.  Air  is 

exhausted  from  the  crown 
of  the  syphon  by  use  of  a 
steam  ejector  whenever  the 
plant  is  to  be  started  up. 
This  plant  operates  under 
the  lowr  head  of  thirty-one 
inches  and  is  said  to  work 
very  satisfactorily. 

Fig.  310  shows  a  vertical 
shaft  turbine  of  the  Victor 
cylindrical  gate  type  man- 
ufactured by  The  Platt 
Iron  Works.  This  wheel 
is  set  in  an  independent 
case  with  provision  made 
for  the  attachment  of  a 
cylindrical  penstock  con- 
ducting the  wrater  from  the 
head  work  to  the  wheel. 
This  figure  shows  a  special 
design  by  which  the  spec- 
ial generator  is  set  on  col- 
umns resting  directly  on 
the  wheel  case. 

Fig.  311  shows  the  plant 
of  Trenton  Falls,  New 
York,  of  the  Utica  Gas  and  Electric  Company.  The  wheel  is  a 
Fourneyron  turbine,  manufactured  by  The  I.  P.  Morris  Company, 
operating  under  a  266  foot  head,  the  water  being  conducted  to  the 
wheel  through  a  penstock  the  length  and  arrangement  of  which  are 
shown  in  Fig.  353.  The  wheel  is  provided  with  a  draft-tube  and  is 
regularly  connected  with  the  generator  above.  The  moving  parts 
of  both  machines  are  carried  by  a  vertical  shaft  bearing,  shown  in  cut. 
255.  Some  Installations  of  Vertical  Wheels  in  Series. — In  the 
last  three  illustrations  wheels  are  shown  of  sufficient  size  and  operat- 


Fig.  310. 


Some  Installations  of  Vertical  Water  Wheels.  511 


Fig.  311.— The  Trenton  Falls  Plant  of  the  Utica  Gas  and  Electric  Co.   (I.  P. 

Morris  Co.) 


512 


Arrangement  of  the  Reaction  Wheel. 


ing  under  sufficient  head  to  be  suitable  for  the  independent  operation 
of  the  machine  attached  to  them.  In  many  cases,  however,  espe- 
cially with  low  head,  the  arrangement  shown  in  Fig.  308  and  in 
Figs.  325  to  329  inclusive,  becomes  necessary.  In  such  cases 
considerable  loss  is  entailed  by  the  use  of  shafts,  gearings,  and  belts. 


Fig.  312.— Vertical  Turbine  for  Sewall's  Falls  Plant  of  the  Concord  Electric  Co. 


These  losses  are  so  large  that  it  is  desirable  to  avoid  or  reduce 
them  if  possible.  For  this  purpose  vertical  wheels  are  sometimes 
placed  tandem  as  shown  in  Diagrams  C  and  D,  Fig.  306.  This 
type  of  plant  is  also  illustrated  by  Figs.  312  and  313  which  are 
illustrative  of  wheels  installed  in  the  plant  of  the  Concord  Electric 
Company,  at  Concord,  N.  H. 


Some  Installations  of  Vertical  Wheels  in  Series. 


513 


Fig.  312  shows  tandem  wheels  for  this  plant  as  designed  and 
manufactured    by    The     Allis-Chalmers    Company    of    Milwaukee, 
..  and  are  described  in  further  detail  on  page 

Fig.  313  is  a  view  of  a 
double  vertical  unit,  designed 
and  built  for  the  Concord 
Electric  Company  by  The  S. 
Morgan  Smith  Company  of 
York,  Pa.  This  form  of  in- 
stallation has  the  advantage 
of  a  greater  concentration  of 
the  machinery.  This  type  of 
installation,  while  quite  com- 
mon in  Europe,  is  somewhat 
new  in  this  country  and  pre- 
sents several  novel  and  desir- 
able features. 

256.  Some  Installations 
of  Horizontal  Water 
Wheels. — Most  machines  to 
be  operated  by  water  wheels 
are  built  with  horizontal  shaft, 
and,  as  a  direct  connection  of 
wheels  to  the  machinery  to 
be  operated  involves  a  min- 
imum loss  in  power  and  con- 
sequent greater  efficiency 
than  with  the  various  com- 
plicated arrangements  often 
necessary  with  vertical 
wheels,  the  horizontal  wheel 
becomes  desirable  and  is 

•adopted  whenever  practicable  in  a  modern  water  power  plant.  The 
type  of  such  a  plant  is  well  illustrated  by  the  power-plant  at  Turner's 
Falls,  Massachusetts,  shown  by  Fig.  314.  The  single  horizontal  wheel, 
•direct-connected  to  th*e  machinery  to  be  operated,  is  perhaps  already 
sufficiently  described  in  the  preceding  pages.  The  arrangement  of 
two  or  more  wheels  for  such  purposes  deserves  careful  consideration. 
Figs.  315  and  316  show  a  plan  and  section  of  a  double  unit,  for  use  in 
an  open  penstock,  as  manufactured  by  The  Dayton  Globe  Iron 
Works  Company  of  Dayton,  Ohio.  These  figures  show  a  plain, 


Fig.  313. 


5i4 


Arrangement  of  the  Reaction  Wheel. 


Some  Installations  of  Horizontal  Water  Wheels. 


cylindrical,  draft-chest  connected  with  a  common  draft-tube.  The 
details  of  the  arrangement  can  perhaps  be  better  seen  from  the  half- 
tone, Fig.  320,  which  illustrates  two  of  these  units  conneted 
together  tandem. 


Fig.  315. — Section  Double  Wheel  with  Common  Draft  Tube.     (Dayton,  Globe 

Iron  Works  Co.) 


Fig.  316.— Plan. 


Figs.  317  and  318  show  a  similar  double  unit  manufactured  by 
the  same  company.  This  unit  is  shown  set  in  a  closed  flume  for 
connection  by  a  penstock  of  suitable  size  with  the  head  works.  In 
Fig.  318  the  chest,  into  which  the  turbines  discharge,  is  designed 
so  as  to  give  a  certain  independence  to-  the  discharge  of  the  two 
turbines  until  they  come  to  the  draft-chest  below  the  wheel.  The 
turbine  case,  shown  in  Fig,  316,  seems  to  have  more  room  than 


516 


Arrangement  of  the  Reaction  Wheel. 


necessary  in  the  upper  portion  of  the  case  in  which  interference  of 
the  two  streams  and  much  eddying  are  possible,  all  of  which  is  ob- 
viated in  the  the  design  .shown  in  Fig.  317.  The  writer  knows  of 
no  experiments  which  show  conclusively  that  such  loss  actually 
occurred.  More  information  is  needed  along  this  line  than  is  now 
accessible  to  the  engineer. 


Fig.  317.— Double  Horizontal  Turbine  in  Closed  Penstock  (Dayton  Globe  Iron 

Works  Co.) 


Fig.  318.— Plan. 

Fig.  319  is  a  cross-section  of  a  double  unit  of  the  Samson  tur- 
bine, manufactured  by  The  James  Leffel  and  Company  of  Spring- 
field, Ohio.  This  shows  a  design  in  which  careful  attention  is 
given  to  the  maintenance  of  a  uniform  and  slowly  decreasing  ve- 
locity from  the  time  the  water  reaches  the  wheel  until  it  passes 
from  the  common  draft-chest  into  the  draft-tube  below. 


Some  Installations  of  Horizontal  Water  Wheels. 


257.  Some  Installations  of  Multiple  Tandem  Horizontal  Wheels. 
— Two  double  units  of  the  wicket  gate  type,  similar  to  the  double 
units  shown  in  Fig.  315,  are  illustrated  by  Fig.  320.  These  turbines 
were  manufactured  by  The  Dayton  Globe  Iron  Company  of  Day- 
ton, Ohio,  and  are  shown  with  the  upper  portion  of  the  case  removed 
so  that  the  arrangement  of  the  wheels  and  the  gate  mechanism  are 
clearly  visible.  The  gates  are  moved  by  a  cylindrical  ring  to  which 


Fig.  319. — Double  Horizontal  Turbine  for  Open  Penstock.    (James  Leffel  &  Co.) 

each  gate  is  attached  independently.  The  ring  is  moved  by  the 
link  connecting  the  gate  ring  to  the  governor  rod  which,  by  its  ro- 
tating, opens  or  closes  the  gate  as  the  power  needed  requires. 

Two  double  units  with  cylindrical  gate,  as  manufactured  by  The 
S.  Morgan  Smith  Company  of  York,  Pennsylvania,  are  shown 
in  Fig.  321.  The  bulkhead  casing  and  the  coupling  to  which  the 
machinery  to  be  operated  must  be  attached,  are  shown  at  the  left. 
In  this  case  the  governor  rods  have  a  horizontal  movement,  the 
upper  rod  moving  backward  and  the  lower  forward  in  order  to 
open  the  cylinder  gate. 

Figs.  322  and  323  show  a  section  through  one  of  the  main  units 
and  a  plan  of  the  power  house  and  turbines  of  The  Soiuthern  Wis- 
consin Power  Company  now  under  construction  at  Kilbourn,  Wis- 
consin, on  the  designs  and  under  the  supervision  of  the  writer. 
This  plant  consists  of  four  main  units,  each  generator  having  a 
capacity,  at  full  load,  of  1650  kilowratts  and  an  overload  capacitv 
of  25  per  cent.  Each  unit  is  direct-connected  to  six  57"  turbines 
now  under  construction  by  The  Wellman-Seaver-Morgan  Com- 


Arrangement  of  the  Reaction  Wheel, 


Soir.e  Installations  of  Horizontal  Water  Wheels.  519 


520  Arrangement  of  the  Reaction  Wheel. 

pany  of  Cleveland,  Ohiou  Each  turbine  unit  is  set  in  a  separate 
penstock  controlled  by  three  independent  sets  of  gates.  The  four 
center  wheels  discharge  in  pairs  into  common  draft-tubes,  while  the 
two  end  wheels  have  independent  draft-tubes.  All  of  the  bearings 
within  the  flume  are  accessible  by  independent  wrought  iron  man- 
hole casings. 

Fig.  324  shows  four  pairs  of  45"  Samson  horizontal  turbines  man- 
ufactured by  The  James  Leffel  and  Company  of  Springfield,  Ohio. 
These  wheels  have  been  installed  for  The  Penn  Iron  Mining  Com- 
pany of  Vulcan,  Michigan,  where  two  such  units  are  now  in  opera- 
tion. Eight  similar  units,  designed -to  deliver  1400  H.  P.  under  14 
foot  head,  are  now  under  construction  by  The  James  Leffel  and 
Company  and  are  to  be  installed  in  the  plant  designed  by  the 
writer  for  The  Economy  Light  and  Power  Company  at  Dresden 
Heights,  Illinois,  the  general  arrangement  of  which  is  shown  by 

Fig.  350. 

When  the  head  increases  above  20  or  30  feet,  it  may  become  de- 
sirable to  convey  the  water  from  the  head-work  by  means  of  a 
closed  penstock  as  shown  in  the  case  of  the  plant  of  The  Winnipeg 
Electric  Railway  Company  (See  Fig.  340). 

In  this  plant  are  shown  four  wheels  in  tandem,  direct  connected 
to  a  generator.  The  bell-mouthed  entrance  to  the  penstock  should 
be  noticed,  also  the  air  inlet  pipe  which  is  designed  to  admit  the 
air  into  the  penstock  when  the  same  is  to  be  emptied,  and  to  admit 
the  water  gradually  and  without  shock  when  it  is  again  filled. 
When  the  head  becomes  still  higher  the  closed  penstock  .becomes 
imperative  as  in  the  case  with  The  Shawinigan  Water  and  Power 
Company's  plant  shown  in  Fig.  338  where  a  head  of  135"  is  utilized. 
Similar  arrangements  and  connections  for  single  and  double  wheels 
with  penstock  are  those  of  The  Dodgeville  Electric  Light  and 
Power  Company,  shown  in  Fig.  337,  and  that  of  The  Hudson  River 
Power  Company's  plant  at  Spier's  Falls,  as  shown  in  Fig.  335. 

The  plant  of  The  Nevada  Power  and  Mining  Company  shown  in 
Fig.  341,  involves  tangential  wheels  operating  with  needle  nozzle 
and  discharging  freely  into  the  tail  race  below. 

In  the  selection  and  installation  of  reaction  wheels  a  con- 
siderable latitude  in  the  choice  and  details  of  arrangement  is  possi- 
ble and  it  is  only  after  a  careful  examination  and  consideration  of 
all  the  conditions  of  installation  that  the  correct  size,  speed,  and 
arrangement  of  the  wheels  can  be  obtained.  Numerous  failures, 
more  or  less  serious,  in  the  past  have  fully  shown  the  fact  that 


Some  Installations  of  Horizontal  Water  Wheels.         '  521 


CM 
CM 

CO 

bo 

B 


522 


Arrangement  of  the  Reaction  Wheel. 


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Some  Installations  of  Horizontal  Water  Wheels. 


523 


524  Arrangement  of  the  Reaction  Wheel. 

this  work  demands  the  most  careful  attention  and  investigation  of 
the  engineer  and  should  be  attempted  only  after  the  most  thor- 
ough study  and  mature  deliberation. 

258.  Unbalanced  Wheels. — In  installing  horizontal  wheels  it  is 
usually  desirable  to  use  them  in  pairs  with  two,  four,  six  or  eight 
turbines  in  tandem.  It  is,  of  course,  possible  to  introduce  an  odd 
number  of  wheels  and  this  is  frequently  done  where  it  seems  to  be 
desirable.  There  is  an  advantage  is  an  even  number  of  wheels  for 
in  this  case  the  wheels  may  be,  and  should  be,  so  arranged  as  to 
balance  the  thrust  by  the  union  of  a  right  hand  and  left  hand  wheel 
in  each  pair.  Where  an  odd  number  of  wheels  is  introduced,  an 
unbalanced  condition  arises  which  can  only  be  taken  care  of  by  a 
thrust-bearing  which,  at  the  best,  is  an  additional  complication 
often  unsatisfactory  and  should  be  avoided  if  possible. 

There  is  another  cause  of  unbalanced  condition  which  may  be 
here  mentioned.  If  a  pair  of  wheels  is  so  joined  together  as  to 
use  a  common  draft-tube  then,  on  starting  the  wheel,  the  vacuum 
formed  in  the  draft-tube  is  co-mmon  to  both  wheels  and  therefore 
balanced.  If,  on  the  other  hand,  the  wheels  have  separate  draft- 
tubes,  when  the  wheels  are  started  a  partial  vacuum  is  commonly 
created  in  one  of  the  draft-tubes  in  advance  of  the  other,  or  even 
when  the  wheels  are  in  operation  the  vacuum  in  one  draft-tube  is 
not  as  great  as  in  the  other,  creating  thereby  a  thrust  in  one  di- 
rection or  the  other  which  must  be  balanced  by  the  connection  of 
the  two  draft-tubes  by  an  air  pipe  or  must  be  taken  up  by  a  thrust- 
bearing  as  in  the  case  of  a  single  wheel. 


CHAPTER  XXI. 

THE  SELECTION  OF  MACHINERY  AND  DESIGN  OF 

PLANT. 

259.  Plant  Capacity. — The   selection  of  machinery  for  a  power 
plant  depends  upon  numerous  conditions.     In  the  first  place,  for 
permanent    and    constant   operation,    the    machinery    must    be    so 
selected  that  its  total  capacity  shall  be  great  enough  to  take  care 
of  the  maximum  load  and  have  at  least  one  unit  in  reserve  so  that 
if  it  becomes  necessary  to  shut  down  one  unit  for  examination  or 
repairs,  the  plant  will  still  be  capable  of  carrying  the  maximum 
load  for  which  it  was  designed. 

The  desirable  reserve  capacity  of  any  plant  depends  on  the  con- 
tingencies of  the  service  or  the  degree  of  liability  to  disabling  acci- 
dent involved  in  the  operation  of  any  plant,  and  on  the  relative 
cost  of  such  reserve  capacity  and  the  damages  which  might  be  sus- 
tained if  the  plant  should  at  any  time  become  disabled  as  a  whole 
or  in  part  and  incapable  of  furnishing  all  or  any  part  of  the  power 
for  which  it  was  designed.  In  many  manfacturing  plants  the  occa- 
sional delays  caused  by  the  entire  suspension  of  power  on  account 
of  high  or  low  water,  or  for  the  necessary  repair  to  machinery,  are 
not  serious  if  cheap  power  is  available  for  the  remainder  of  the 
year.  For  the  operation  of  public  utilities,  and  the  furnishing  of 
light  and  power  for  diverse  municipal  and  manufacturing  purposes, 
the  matter  becomes  more  serious  and  necessitates  a  sufficient  du- 
plication of  units  to  practically  assure  continuous  operation. 

For  paper  mills  and  other  manufacturing  purposes  water  powers 
are  utilized  in  which  the  head  and  consequent  power  is  practically 
destroyed  during  high  water  conditions.  For  continuous  and  un- 
interrupted service  such  powers  are  available  only  with  auxiliary 
power  that  can  be  used  during  such  periods.  In  the  same  manner 
reserve  capacity  may  be  unnecessary,  desirable  or  absolutely  essen- 
tial as  the  importance  of  maintaining  uninterrupted  power  in- 
creases. 

260.  Influence  of   Choice  of  Machinery  on  Total  Capacity. — A 
study  of  the  week  day  load  curve  of  The  Hartford  Electric  Light 

32 


526  The  Selection  of  Machinery  and  Design  of  Plant. 

Company  as  shown  by  Fig.  257,  page  422,  will  show  that  the  load 
for  December,  1901,  represents  the  maximum  load  which  that  plant 
was  called  upon  to  carry  during  the  year,  and,  consequently,  was 
the  maximum  load  for  which  the  machinery  must  have  been  se- 
lected. A  considerable  variety  of  unit  sizes  would  be  possible 
which  would-  fill  the  requirements  of  this  load  curve  to  a  greater 
or  less  extent.  The  maximum  or  peak  load  shown  in  December, 
1901,  was  about  3,000  k.  w.  If  a  single  machine  were  selected  of 
3,000  k  w.  capacity  for  regular  operation,  then,  in  order  to  have 
one  unit  in  reserve,  it  would  be  necessary  to  purchase  two  3,000 
k.  w.  machines  or  a  total  capacity  of  about  6,000  k.  w.  If,  on  the 
other  hand,  machinery  should  be  purchased  with  units  of  500 
k.  w.  capacity  each,  it  would  be  necessary  to  have  six  of  such  units 
in  order  to  carry  the  maximum  load  of  3,000  k.  w.,  and  a  seventh 
unit  of  500  k.  w.  capacity  would  be  all  that  would  be  needed  for  the 
reserve.  This  would  give  a  total  capacity  to  the  plant  of  3,500  k.  w., 
giving  the  capacity  of  the  machine  purchased  some  2,500  k.  w. 
less  than  the  plant  first  discussed. 

261.  Effect  of  Size  of  Units  on  Cost. — The  cost  of  machinery  is 
not  in  direct  proportion  to  its  capacity.     The  larger  machinery  is 
somewhat  less  in  price  per  kilowatt  capacity  than  the  smaller  ma- 
chinery.   Hence  the  cost  of  the  last  plant  suggested  would  be  more 
than  35/60  of  the  cost  of  the  first  plant.    On  the  other  hand,  the  in- 
stallation of  such  a  large  number  of  units  complicates  the  plant  and 
is  undesirable.     For  this  plant  it  would  therefore  be  desirable  to 
select  five  units  of  750  k.  w.  capacity  each,  or  four  units  of  1,000 
k.  w.  capacity  each,  giving  in  one  case  a  total  plant  capacity  of 
3,750  k.  w.  and  in  the  other  case  of  4,000  k.  w. 

A  plant  having  units  of  750  k.  w.  or  1,000  k-  w.  capacity  each 
would  have  a  less  total  kilowatt  capacity  and,  consequently,  a  less 
first  cost  compared  with  a  plant  having  units  of  3,000  k.  w.  capacity. 
Such  a  plant  would  also  have  a  less  number  of  units  and  conse- 
quently less  complication  in  the  arrangement  than  a  plant  having 
units  of  500  k.  w.  capacity. 

262.  Overload. — In  the  above  consideration  no  mention  is  made 
of  overload  capacity.     The  ordinary  direct-current  machinery  can 
be  operated  at  about  25  per  cent,  overload  for  short  periods  of  per- 
haps one  hour  at  a  time  without  danger  to  the  machinery.    Alter- 
nating machinery  can  be  operated  at  50  per  cent,  overload  at  similar 
times  or  at  25  per  cent,  overload  for  two  hour  periods.    In  conse- 
quence of  this  condition  it  is  frequently  possible  to  purchase  ma- 


Economy  in  Operation.  527 

chinery  of  considerable  less  capacity  than  the  total  load  would  in- 
dicate, depending  on  the  overload  capacity  of  the  machine  for  short 
periods  of  maximum  load.  Unless,  however,  the  estimated  load 
curve  covers  all  possible  contingencies  for  maximum  power  it  is 
desirable  to  retain  this  overload  capacity  as  a  provision  for  a  second 
condition  which  has  not  been  fully  covered  in  the  estimate  of  the 
daily  load  curve ;  or,  in  other  words,  it  is  desirable  to  retain  the 
overload  capacity  as  a  factor  of  safety. 

263.  Economy  in  Operation. — A  second  matter  that  needs  the 
careful  consideration  of  the  engineer  in  the  selection  of  machinery 
is  the  question  of  economic  operation  under  variation  in  load.  A 
reference  to  the  efficiency  curve  of  most  machines  will  show  that 
the  machine  will  operate  most  efficiently  at  some  particular  load, 
usually  some  .75  to  full  load,  and  will  perhaps  give  the  best  results 
at  from  .75  to  1.25  load,  or  to  25  per  cent,  overload.  It  therefore 
becomes  important  to  so  select  machinery  that  it  will  operate  effi- 
ciently at  all  conditions  of  Joad. 

An  examination  of  the  load  curve  of  The  Hartford  Electric  Light 
Company  for  the  full  week  day  load  in  March,  June,  September 
and  December,  will  show  that  for  securing  the  most  efficient  results 
at  all  times  in  the  day,  and  at  all  times  in  the  season,  units  of  500 
k.  w.  capacity  would  apparently  be  the  best.  Such  units  would 
take  care,  efficiently,  of  the  minimum  loads  that  occur  at  6  :oo 
A.  M.,  between  12:00  and  I  :oo  P.  M.,  and  at  about  7:00  P.  M.  At 
such  times  one  of  these  units  would  operate  efficiently;  but  in 
most  cases  the  period  at  which  it  could  be  operated  singly  would 
be  for  a  few  minutes  only,  or  perhaps  for  an  hour  at  the  most,  when 
the  additional  unit  would  have  to  be  cut  in.  A  750  k.  w.  generator 
would  operate  with  almost  as  great  an  efficiency  at  these  times  and 
it  would,  with  its  overload  capacity,  take  care  of  the  load  for  a  much 
greater  period  of  time  each  day.  The  1,000  k.  w.  machine  would 
perhaps  fulfill  these  requirements  even  to  a  greater  degree.  While 
it  would  be  less  efficient  at  the  minimum  point  of  the  load,  it  would 
have  the  advantage  of  operating  singly  for  a  much  wider  range  of 
load  and  the  additional  advantage  that,  as  a  rule,  the  larger  the  ma- 
chine the  higher  the  full  load  efficiency  curve. 

The  complications  resulting  from  the  numerous  machines,  and 
the  losses  entailed  thereby,  have  also  to  be  considered  and  must  be 
carefully  weighed  in  this  connection. 

The  circumstances  of  operation  and  many  local  conditions,  which 
appertain  particularly  to  the  plant  in  question,  must  be  weighed  in 


528  The  Selection  of  Machinery  and  Design  of  Plant. 

connection  with  the  selection  of  this  machinery.  There  is  no  defi- 
nite law  by  which  the  selection  of  machinery  for  any  plant  can 
be  reduced  to  an  exact  science,  and  several  combinations  of  ma- 
chinery are  possible  in  almost  any  plant  and  will  give  reasonable 
satisfaction. 

In  the  above  discussion  only  units  of  a  uniform  capacity  have 
been  considered  and  it  is  usually  desirable,  other  things  being  equal, 
to  have  similar  machines  so  that  a  minimum  number  of  repairs 
and  duplicate  parts  may  be  kept  in  stock.  On  the  other  hand,  if  a 
long,  low  night  load  is  probable,  it  may  be  desirable  to  install  one 
or  more  units  of  a  capacity  suitable  to  carry  such  load  efficiently. 

264.  Possibilities    in    Prime    Movers. — A   third   matter  for   the 
careful  consideration  of  the  designing  engineer  is  the  possibility 
of  a  prime  mover  that  is  to  be  used  for  operating  the  machines  in 
question.     If  a  steam  or  gas  engine  is  to  be  used  as  the  motive 
power,  there  is  a  wide  range  of  selection  in  speed,  capacity,  and 
economy  of  such  machinery,  and,  as  a  general  rule,  the  prime  mover 
may  be  selected  to  conform  to  the  generator  or  other  machine  that 
is  to  be  operated  thereby.     In  the  selection  of  water  wheels  for 
prime  movers  the  conditions  are  radically  different  and  the  selection 
of  the  size  and  capacity  of  the  units  to  be  operated  is  "often  modi- 
fied or  controlled  by  the  waterwheels  and  the   conditions   under 
which  they  will  be  obliged  to  operate. 

In  the  selection  of  the  water  wheel  one  of  the  most  important 
matters  is  the  head  and  the  range  of  heads  under  which  the  wheel 
will  be  called  upon  to  operate.  While  it  is  possible  to  select  a  wheel 
so  that  it  will  operate  at  almost  any  reasonable  speed  under  a  con- 
siderable head,  yet  the  capacity  or  power  of  the  wheel  rapidly  de- 
creases in  amount  with  the  speed,  and  if  the  speed  be  too  high  it 
will  be  necessary  to  join  two  or  more  wheels  in  tandem  in  order  to 
furnish  the  power  necessary  to  operate  the  machinery  selected. 
This  is  perfectly  feasible  and  is  done  in  a  great  many  cases. 

265.  Capacity  of  Prime  Movers. — It  is  important  to  note  that  if 
the  generator  or  other  machinery  to  be  operated  is  to  be  operated 
under  overload  conditions,  the  maximum  power  to  be  generated 
must  be  kept  fully  in  mind  in  the  selection  of  a  prime  mover.     In 
the  case  of  steam  engines,  these  engines  can  be  commonly  operated 
under  overload  conditions.     They  are  usually  rated  at  their  most 
efficient  capacity  and  can  sometimes  be  operated  to  50  per  cent. 
above  their  normal  rating,  although  their  economy  under  such  con- 
ditions is  apt  to  materially  decrease.     Gas  engines,  on  the  other 


Power  Connection.  529 

hand,  are  commonly  rated  at  very  nearly  their  full  capacity  and 
hence  the  machinery  which  they  are  to  operate  can  be  operated  only 
to  about  the  normal  rated  capacity  of  the  engine. 

Water  wheels  are  commonly  rated  in  the  catalogues  of  manu- 
facturers at  very  nearly  full  gate  and  consequently  at  full  power. 
In  some  cases  they  are  rated  at  about  seventh-eighths  gate  so  that 
a  small  margin  of  additional  power  is  availalble.  In  the  selection 
of  a  water  wheel,  therefore,  it  is  important  that  a  careful  study 
be  made  of  the  actual  power  that  the  wheel  can  generate  under  full 
gate  and  at  minimum  head.  This  should  be  sufficient  to  operate  the 
machinery  at  its  maximum  load. 

266.  The  Installation  of  Tandem  Water  Wheels.— The  installa- 
tion of  two  wheels  set  tandem,  either  horizontally  or  vertically, 
and  directly  connected  with  the  machine  by  a  common  shaft,  is 
very  common  and  this  may  be  increased  to  four,  six,  or  occasionally 
to  eight  turbines.    Every  additional  machine,  however,  involves  the 
introduction  of  increased  diameter  in  the  shaft,  of  additional  bear- 
ings which  must  be  set  and  held  in  alignment,  and  a  complica- 
tion in  the  design  and  construction  of  the  machinery  which  should 
be  avoided  wherever  possible.    The  excuse  for  the  attachment  of  a 
number    of    turbines    in    tandem    arrangement,    and     the     com- 
plexity  of  the   plant   of   water  wheels   installed,   lies   in   the   sim- 
plification of  the  machinery  to  be  operated  by  them,  and  in  the  de- 
sign and  arrangement  of  other  portions  of  the  plant.     The  extent 
to  which  the  application  of  any  principle  is  to  be  carried  is  a  matter 
of  judgment  and  can  be  answered  only  by  experience  and  the  con- 
sideration of  all  of  the  conditions  involved  in  each  particular  case. 

267.  Power  Connection. — -With  the  turbine,  as  with  every  other 
prime  mover,  it  is  important  to  convey  the  power  to  the  machine 
or  machinery  to  be  operated  as  directly  as  possible.    The  turbines 
should  be  connected  as  directly  as  possible  to  the  machinery  to  be 
driven  without  any  unnecessary  intervention  of  gearing,  shafting, 
bearings,  belts,  cables,  or  other  still  more  complicated  methods  of 
power  transmission.     Every  shaft,   every  gear,  every  belt,   every 
bearing  and  every  other  means  of  transmission  that  intervenes  be- 
tween the  power  generated  in  the  wheel  and  the  machine  in  which 
the  power  is  to  be  utilized  means  an  extra  loss  and  a  decrease  in 
the  efficiency  of  the  plant.     The  machine  to  be  operated  should, 
therefore,  whenever  practicable,  be  direct  connected  to  the  shaft 
of  the  turbine  instead  of  being  connected  with  the  turbine  by  any 
intermediate    mechanical    means.     (See    Figs.    310,   314   and   322— 


530  The  Selection  of  Machinery  and  Design  of  Plant. 


Various  Methods  of  Connection.  531 

Direct  connection  of  machinery  and  turbine  involves  a  careful  selec- 
tion of  both  machinery  and  turbine  so  that  both  will  work  satis- 
factorily at  the  same  number  of  revolutions  per  minute.  This 
frequently  involves  extra  expense  that  may  not  be  justified  in  plants 
for  many  purposes. 

Other  methods  of  connection  or  of  power  transmission  are, 
therefore,  frequently  necessary.  With  many  low  head  installations 
direct  connections  are  impracticable  for  a  number  of  reasons. 
Sometimes  various  machines  with  diverse  revolutions  are  to  be 
driven  by  the  same  wheel  and  the  revolutions  of  the  turbines  in- 
stalled must  differ  from  some  or  all  of  the  machinery  to  be  operated 
and  some  form  of  connection  other  than  the  direct  must  be  used. 
Even  where  the  importance  of  the  plant  makes  it  desirable  to  use  di- 
rect connection,  it  frequently  happens  that  a  single  turbine  gives 
an  insufficient  power  at  the  speed  desirable  for  connection  to  a 
machine  of  the  desired  capacity.  Under  such  conditions  it  is  nec- 
essary to  unite  two  or  more  turbines  in  order  to  generate  sufficient 
power  for  the  purposes  for  which  the  plant  is  to  be  designed.  The 
necessity  of  using  a  large  number  of  turbines  in  a  single  unit  may 
give  rise  to  very  long  shafts  and  a  large  number  of  bearings,  and 
the  loss  due  to  such  an  arrangement  is  sometimes  considerable,  and 
if  poorly  arranged  will  be  almost  or  quite  as  inefficient  as  gearings 
and  shafting  well  maintained. 

268.  Various  Methods  of  Connection  in  Use. — The  most  common 
form  of  turbine  used  is  a  single  vertical  turbine,  connected  by  a 
beveled  crown  gear  and  pinion  to  a  horizontal  shaft.  Several  of 
such  turbines  are  commonly  coupled  up  to  the  same  shaft  and  may 
be  set  in  a  single  or  in  separate  wheel  pits.  Such  types  of  installa- 
tion are  shown  in  Figs.  329  to  334.  Fig.  325  shows  the  turbine 
harness  in  the  plant  of  The  Oliver  Plow  Works  at  South  Bend, 
Indiana,  installed  by  The  Dodge  Manufacturing  Company.  The 
arrangement  of  the  wheel  is  quite  similar  to  that  illustrated  by 
Fig.  334.  Three  or  four  vertical  wheels  are  here  each  connected 
by  a  gear  and  pinon  with  a  horizontal  shaft,  which,  in  turn,  is  con- 
nected to  an  electric  generator.  In  all  such  cases  more  or  less 
energy  is  lost  in  transmitting  the  power  through  the  gearing  and 
numerous  bearings  to  the  generator.  Sometimes  it  is  found  desir- 
able not  to  connect  the  generators  directly  with  the  main  shaft, 
but  to  connect  the  generator  or  other  machines  to  be  operated  by 
the  power  plant  by  belting  them  to  driving  pulleys  attached  to  the 
same  horizontal  shaft,  as  shown  by  Fig.  326,  which  shows  the  power 


532  The  Selection  of  Machinery  and  Design  of  Plant. 


Various  Methods  of  Connection. 


533 


plant  of  The  Trade  Dollar  Mining-Company  near  Silver  City,  Idaho. 
This,  however,  introduces  another  source  of  loss  through  these 
belts  but  possesses  a  certain  flexibility  due  to  the  ability  to  thereby 
drive  various  small  units  at  a  variety  of  speeds  by  the  simple  process 
of  changing  the  diameter  of  the  pulleys  used  to  drive  such  machin- 
ery. Sometimes  rope  drives  can  be  used  to  advantage  in  place  of 


Fig.  327. — Harness  and  Driving  Sheaves,  Southwest  Missouri  Light  Co., 

Joplin,  Mo.* 

belts.  This  is  especially  true  where  the  distance  is  great  or  the 
alignment  other  than  direct.  Examples  of  such  connections  are 
shown  by  Figs.  327  and  328. 

Direct  connected  plants  are  shown  in  Figs.  310,  314,  322,  335,  etc. 

269.  Use  of  Shafting. — A  shaft  connecting  a  machine  to  a  prime 
mover,  or  imposed  in  any  manner  in  any  power  transmission,  must 
be  carefully  designed  and  constructed.  It  must  be  carefully  aligned 
and  have  its  bearings  carefully  adjusted.  Each  bearing  may  be  con- 
sidered as  a  point  in  the  alignment  of  a  shaft,  and,  as  two  points 
determine  the  direction  of  a  straight  line,  it  will  be  seen  that  each 
additional  bearing  is  objectionable  for  it  increases  the  difficulty  of 
obtaining  and  maintaining  a  satisfactory  alignment.  When  more 
than  two  bearings  are  used  each  must  be  brought  and  maintained  in 

*  Dodge  Manufacturing  Co., .  Mishawaka,  Ind. 


534  The  Selection  of  Machinery  and  Design  of  Plant. 

the  best  practicable  alignment,  both  horizonally  and  vertically.  All 
bearings  must  be  of  sufficient  size  that  the  limit  of  bearing  pres- 
sure shall  not  exceed  good  practice  and  they  must  be  sufficiently 
adjustable  so  that  the  shaft  shall  have  as  complete  and  uniform  bear- 


Fig.    328. — Plan    Showing   Harness,  Rope   Drive    and   Jackshaft.     Southwest 

Missouri  Light  Co.* 

ing  as  possible  over  the  entire  surface  of  the  box.  Boxes  and  bear- 
ings must  be  arranged  for  satisfactory  lubrication  so  that  under 
the  hardest  service  they  will  not  become  unduly  heated.  In  order 
to  secure  good  results  the  best  class  of  workmanship  is  necessary 
and  it  is  also  necessary  that  the  plant  shall  be  carefully  and  prop- 

*Dodge  Manufacturing  Co. 


The  Wheel  Pit.  535 

erly  maintained.  A  poor  shaft,  running  in  poor  boxes,  poorly 
aligned,  may  consume  most  of  the  power  generated.  Shafting,  to 
be  reasonably  satisfactory,  demands  frequent  and  proper  inspection, 
constant  lubrication,  and  proper  maintenance  or  it  will  soon  become 
a  source  of  great  energy  loss. 

270.  The  Wheel  Pit. — The  wheel  is  usually  set  in  a  chamber 
called  the  wheel  pit,  flume,  or  sometimes  the  penstock,  which  is 
connected  with  the  head-race  from  which  it  can  be  separated  by 
suitable  gates. 

The  wheel  pit  in  the  smaller  plants  has  commonly  been  con- 
structed of  timber  but  in  the  larger  plants  is  usually  built  of  a  more 
substantial  character, — of  concrete,  plain  or  reinforced,  stone  or 
iron. 

Open  pits  are  commonly  used  for  heads  up  to  18  or  20  feet,  and 
may  be  used  for  considerably  higher  heads ;  however,  for  higher 
heads,  closed  flumes  of  reinforced  concrete  or  steel  are  commonly 
used,  and  such  construction  is  usually  connected  with  the  head- 
race by  metal,  wood  or  reinforced  pipes,  to  which  the  term  penstock 
is  commonly  applied.  This  latter  form  of  construction  admits  of 
the  use  of  wheels  with  heads  of  almost  any  height. 

A  number  of  wheels  can  be  set  in  the  same  wheel  pit,  and  are 
commonly  so  set,  especially  where  they  are  used  together  to 
operate  one  machine.  It  is  frequently  desirable,  however,  to  sep- 
arate the  turbines  and  set  them  in  separate  pits  so  that  one  or 
more  wheels  can  be  shut  down  at  any  time  without  interfering 
with  the  operation  of  the  plant.  The  exent  to  which  this  arrange- 
ment is  carried  is  a  matter  of  policy  and  depends  upon  a  variety  of 
conditions  which  the  engineer  must  settle  for  each  particular  case. 

271.  Turbine  Support. — The  arrangement  and  construction  of  the 
wheel  pit  must  be  such  as  to  furnish  a  proper  support  for  the  tur- 
bine in  order  to  secure  satisfactory  operation.     In   many  of  the 
earlier  plants,  the  wheel  pits  were  built  of  timber,  with  the  turbine 
case  resting  direc.tly  on  the  timber  floor,  which  was  often  improp- 
erly supported.    The  result  of  such  conditon  has  been  that  the  tur- 
bines settle  out  of  alignment  and  much  energy  is  expended  in  un- 
due friction  in  the  transmitting  mechanism.     The  floor  or  founda- 
tion on  which  the  wheel  case  rests  should  be  of  a  substantial  char- 
acter and  of  such  a  nature  that  it  will  not  readily  deteriorate  and 
allow  the  wheel  to  settle.     It  is  usually  desirable  to  support  the 
wheel  by  a  column  directly  below  the  wheel  case,  which  should  rest 
upon    substantial    foundations  below  the  bottom   of  the    tail-race, 


536  The  Selection  of  Machinery  and  Design  of  Plant. 

(See  Fig.  331)  In  all  events  settlements  and  vibrations  must  be 
prevented  or  reduced  to  a  minimum  in  order  to  eliminate  one  of  the 
very  important  causes  of  loss  which  is  frequently  encountered  in 
water  power  plants.  In  many  cases,  due  to  defects  of  this  kind, 
water  power  plants  are  giving  efficiencies  of  50  per  cent,  and  below, 
where  75  or  80  per  cent,  should  be  obtained. 

272.  Trash  Racks. — The  water  entering  the  wheel  pit  from  the 
head-race  commonly  passes  through  a  trash  rack  consisting  of  nar- 
row bars  of  iron,  usually  y±"  by  3"  in  dimension,  spaced  i1/^"  to  2" 
between  and  reaching  from  above  the  head-waters  to  the  bottom  of 
the  wheel  pit,  the  purpose  of  which  is  to  strain  out  such  floating 
matter  as  may  be  brought  by  the  current  down  the  head-race  and 
which,  if  not  taken  out  at  this  point,  might  float  into  the  wheels 
and  if  large  and  heavy  enough,  might  seriously  injure  the  same. 
These  racks  'have  to  be  raked  or  cleaned  out  at  intervals  depending 
on  the  amount  of  leaves,  grass,  barks,  ice  or  other  floating  matter 
in  the  stream.  In  water  power  plants  on  some  streams  where  large 
amounts  of  such  floating  matter  occurs  at  certain  seasons,  it  is 
sometimes  necessary  to  keep  a  large  number  of  men  constantly 
at  work  keeping  the  racks  clear. 

The  accumulation  of  material  on  the  racks  will  sometimes  shut 
off  the  entire  flow  of  water  if  attention  is  not  given  to  keeping  them 
clear;  hence  it  is  sometimes  necessary  to  so  design  the  racks  and 
their  supports  that  they  may  sustain  the  entire  head  of  water. 

The  racks  are  usually  made  of  barb  wire  held  apart  by  spools  be- 
tween each  pair  of  bars  and  held  together  by  bolts  passing  through 
the  spools  and  joining  together  such  a  number  of  bars  as  may  be 
convenient  for  handling.  The  spools  should  usually  be  placed  near 
the  back  of  the  bar  so  as  to  allow  the  rake  teeth  to  pass  readily. 
.The  rack  should  be  situated  at  an  angle  so  as  to  afford  facilities 
for  raking.  The  deeper  the  water,  the  greater  should  be  the  in- 
clination, as  with  long  racks,  and  especially  with  high  velocities,  the 
clearing  of  the  racks  becomes  more  difficult. 

Chain  racks  and  automatic  mechanical  racks  have  been  attempted 
but  without  satisfactory  results. 

Where  trouble  occurs  from  ice,  involving  much  winter  work,  it 
is  frequently  desirable  to  cover  the  racks  with  a  house  in  order  to 
protect  the  workmen. 


CHAPTER  XXII. 

EXAMPLES  OF  WATER  POWER  PLANTS. 

273.  Sterling  Plant.— A  rear  elevation    (Fig.   329)    of  the  plant 
which  was  designed  by  the  writer  for  The  Sterling  Gas  and  Electric 
Company  of  Sterling,  Illinois,  shows  three  50"  vertical  Lefrel  wheels 
connected  to  a  common  shaft  by  beveled  gearings. 

The  general  type  of  harness  used  is  fully  shown  in  the  plan  and 
elevation  and  needs  no  further  description. 

This  plant  is  located  on  the  Sterling  race  and  is  next  to  the  last 
plant  on  the  race  on  the  Sterling  side  of  Rock  River.  (See  Fig.  345.) 
The  head  developed  at  this  plant  is  about  8  feet,  and  the  power  of 
each  wheel  is  about  115  horse  power.  Each  wheel  is  set  in  an  inde- 
pendent wheel  pit  which  can  be  closed  by  means  of  a  gate,  as  shown 
in  Fig.  332.  In  order  to  make  repairs  on  any  wheel  without  inter- 
fering with  the  other  wheels,  the  wheels  and  harness  are  well  sup- 
ported from  the  foundation,  a  very  essential  condition  for  perma- 
nently maintaining  a  high  efficiency.  The  discharge  pit  is  of  ample 
size,  so  that  the  velocity  with  which  the  escaping  waters  leave  the 
draft  tube  is  reduced  to  a  practical  minimum.  A  rack,  to  keep 
coarse  floating  material  from  the  wheel,  is  placed  in  front  of  the 
penstock  and  is  shown  in  Fig.  331,  in  section,  and  in  Fig-  332, 
in  partial  elevation.  The  shaft  ojf  this  plant  is  extended  into  the 
adjacent  building  and  to  it  are  belted  the  generators  which  supply 
electric  current  for  light  and  power  purposes  in  the  city  of  Sterling. 
An  engine  is  also  connected  to  this  main  shaft  and  may  be  utilized 
in  case  of  extreme  low  water  conditions,  where  sufficient  water  for 
power  is  not  available,  or  for  flood  conditions  where  the  head  is 
practically  destroyed. 

274.  Plant  of  York-Haven  Water  Power  Company. — Figure  333 
shows  the  arrangement  of  the  power  station  of  the  York-Haven 
Water  Power  Company  on  the  Susquehanna  River  at  York,  Pa. 

The  power  house  is  478  ft.  long  and  51  ft-  wide.  The  head-race 
is  500  ft.  long  and  of  an  average  depth  of  20  ft.  The  wheel  pits  are 
19  ft.  deep  and  extend  the  entire  width  of  the  power  house,  open- 


538 


Examples  of  Water  Power  Plants. 


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Plant  of  the  Sterling  Gas  and  Electric  Light  Co.  539 


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Examples  of  Water  Power  Plants. 


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Fig.  331.— Wheel  Pit,  Sterling  Gas  and  Electric  Light  Co.'s  Plant. 


Plant  of  the  Sterling  Gas  and  Electric  Light  Co.  541 


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542 


Examples  of  Water  Power  Plants. 


ing  to  the  forebay.  They  are  protected  by  iron  racks  and  are  made 
accessible  by  large  head-gates  of  structural  iron  which  weigh  about 
eleven  tons  each. 


Fig.  333— Plant  of  York  Haven  Water  Power  Co. 
(Electrical  Engineer.) 

Each  pit  contains  two  78.5"  inward  flow  turbines,  hung  from 
spring  bearings  just  above  the  runners.  The  turbines  are  set  on  the 
floor  of  the  pit  and  are  about  6  ft.  above  the  lower  water  mark. 

The  draft  tubes  are  10  ft.  long  and  extend  well  under  water.  The 
net  head  under  normal  conditions  is  about  21  ft.  Float  gauges  on 
the  switch  board  show  at  a  glance  the  height  of  head  and  tail 
water. 


Plant  of  South  Bend  Electric  Company.  543 

The  turbines  were  built  by  the  Poole  Engineering  Company  of 
Baltimore,  Mr.,  and  are  rated  at  550  H.  P.  each,  or  1,100  H.  P.  per 
pair. 

The  turbines  are  of  special  design,  the  buckets  being  made  of 
pressed  steel.  The  shaft  extends  vertically  from  the  turbines  to 
bevel  gears  above  the  main  floor  and  each  is  encased  in  a  cast  iron 
tube  to  protect  it  from  the  action  of  the  water  and  to  secure  long- 
evity both  to  the  shaft  and  to  the  bearings  which  retain  it  in  line. 

The  present  installation  consists  of  ten  pairs  of  turbines  with 
ten  generators,  equipped  with  Sturgess  and  Lombard  governors. 

The  turbine  bearings  are  supplied  with  oil  from  a  gravity  tank 
located  on  the  switch-board  gallery  . 

The  generators  are  S.  K.  C,  three-phase,  60  cycle  alternators, 
rated  at  875  kilowatts,  and  generate  a  2,400  volt  current.  The  nor- 
mal speed  of  the  generators  is  200  revolutions  per  minute.  Two  250 
K.  W.,  125  volt,  S.  K.  C.,  compound-wound,  direct-current  exciters 
furnish  the  exciter  current  to  the  generator  fields.* 

275.  Plant  of  South  Bend  Electric  Company. — Figure  334  shows 
the  plant  of  the  South  Bend  Electric  Company  at  Buchanan,  Mich- 
igan, built  in  1901. 

The  dam,  which  was  constructed  in  1895,  is  of  the  gravity  type, 
built  of  wood,  with  two  rows  of  sheet  piling  below  and  one  above 
it.  It  is  about  400  feet  long,  and  affords  an  average  head  of  10  feet. 
This  is  estimated  to  furnish  a  minimum  of  2,000  h.  p.  for  from 
four  to  six  weeks  in  a  year,  while  the  maximum  will  reach  5,000  h.  p. 
On  an  average,  2,500  h.  p.  is  available  for  about  three  months  and 
4,000  h.  p.  for  the  remainder  of  the  year. 

The  power  house,  placed  a  short  distance  below  the  dam,  is  273 
feet  long  and  40  feet  wide.  It  is  built  of  stone,  with  concrete  foun- 
dations, and  slate  roof.  It  parallels  the  river  so  that  the  water  from 
the  turbines  is  discharged  directly  into  the  same.  The  regulating 
gates  are  seven  in  number,  and  are  operated  by  racks  and  pinions. 

The  water  wheels  are  Leffel  turbines  of  68  inch  vertical  type, 
300  h.  p-  each.  They  are  geared  to  a  line  shaft,  which  extends  nearly 
the  whole  length  of  the  building,  and  to  the  end  of  which  the  genera- 
tor is  coupled.  A  40  inch  vertical  Leffel  wheel  is  used  for  driving  the 
exciter,  which  is  belted  to  an  intermediate  shaft,  driven  by  gears. 
The  line  shaft  is  divided  into  three  units,  so  that  either  four,  seven 
or  ten  wheels  can  be  used  for  operating  the  generator,  depending 

*  See  Electrical  World,  vol.  49,  March  2nd,  1907. 


544 


Examples  of  Water  Power  Plants. 


Spier's  Falls  Plant  Hudson  Water  Power  Co. 


545 


upon  the  load  carried.  In  addition,  the  gears  on  the  line  shaft  can 
be  thrown  out  of  mesh,  so  that  any  water  wheel  can  be  repaired  if 
necessary.  The  plant  is  governed  by  two  Lombard  water  wheel 
governors  driven  from  the  line  shaft. 

A  20  ton  hand-operated  crane  serves  all  the  apparatus  in  the 
building. 


Fig.  335. — Plant  of  Hudson  Water  Power  Co.     Spier's  Falls  Plant.     Double 
Horizontal  Turbines  in  Steel  Penstock.     Central  Discharge.    (Engine- 
ering Record.) 

The  generator  is  a  1,500  k.  w.,  60  cycle  General  Electric  revolving 
field  type  alternator  supplying  three-phase  current  at  a  pressure  of 
2,300  volts.  The  switch-board  and  transformers  are  located  at  one 
end  of  the  building.  There  are  no  high  tension  switches  at  the 
power  house. 

The  power  is  largely  transmitted  to  South  Bend,  Indiana,  a 
distance  of  16  miles,  where  the  company  has  a  steam  power  plant 


546  Examples  of  Water  Power  Plants. 

which  is  always  kept  in  such  condition  as  to  be  put  into  immediate 
operation.  It  is  used,  however,  only  in  case  of  extreme  low  water, 
at  times  of  a  heavy  peak,  or  in  case  of  accident  to  the  transmission 
line.  The  steam  power  house  is  used  as  a  sub-station  and  distrib- 
uting point.* 

276.  Spier  Falls  Plant  of  The  Hudson  River  Power  Transmission 
Company. — A  cross  section  of  the  Spier  Falls  Power  house  is  shown 
in  Fig.  335.    A  head  of  75  feet,  for  operation  of  this  plant,  is  derived 
from  a  granite  rubble,  ashlar-faced,  masonry  dam  across  the  Hud- 
son River  between  Mount  McGregor  and  the  Luzerne  Mountains. 
The  dam  consists  of  817  feet  of  spillway  section,  the  remainder 
of  the   dam,   552  feet,   being  built  about   12   feet   higher.     Water 
is  admitted  through  arched  gateways  to  a  short  intake  canal  de- 
signed to  carry  6,000  cubic  feet  per  second  with  a  velocity  of  three 
feet  per  second.    This  canal  distributes  the  water  to  ten  12'  circular 
steel  penstocks  which  lead  about  150  feet  to  the  wheels. 

The  power  house  is  divided  into  three  parts  with  the  transformer 
and  switchboard  room  in  one  end,  the  wheel  room  and  generator 
room  being  formed  by  a  longitudinal  partition  wall  extending  the 
length  of  the  building,  with  traveling  crane  in  each. 

Each  unit  consists  of  a  pair  of  42"  or  54"  cased  S.  Morgan  Smith 
wheels,  governed  by  Lombard  and  Sturgess  governors  and  direct 
connected  to  2,000  and  2,500  k.  w.  40  cycle,  three-phase  revolving 
field  generators,  built  by  The  General  Electric  Company. 

The  transformer  room  contains  seven  670  k.  w.  and  thirty  833 
k.  w.  General  Electric  air  cooled  transformers. 

The  power  is  distributed  to  Glen  Falls,  Schenectady,  Saratoga 
Springs  and  Albany,  f 

277.  Plant   of   Columbus   Power   Company. — The    plant   of   the 
Columbus  Power  Company  is  shown  in  Fig.  336.     It  is  situated  on 
the  Chattahoochie  River  just  beyond  the  limits  proper  of  the  city 
of  Columbus,  Georgia,  at  a  shoal  known  as  Lovers'  Leap.     At  this 
point  a  dam  of  cyclopean  or  boulder  concrete  with  a  cut  stone  spill- 
way surface  was  erected  giving  a  head  of  40  feet.    The  length  of  the 
dam  is  975  feet  8  inches,  with  a  spillway  728  feet  long. 

The  power  house  is  located  at  one  end  of  the  dam,  so  that  no  pen- 
stocks are  necessary.  This  applies  to  power  house  No.  I.  Power 

to  drive  the  plant  of  The   Bibb  Manufacturing  Company  is  fur- 

. 

*|See  Electrical  World  and  Engineer,  May  30,  1903  and  July  14,  1906. 
fSee  Engineering  Record,  June  27th,  1903. 


Plant  of  Columbus  Power  Co. 


547 


nished  from  power  house  No.  2,  being  transmitted  to  the  mill  by  a 
rope  drive  system.  The  power  house  is  supplied  with  pressure 
water  by  means  of  penstocks  let  through  the  bulk-head  wall,  which 
extends  from  house  No.  I  to  the  river  bank.  In  both  cases  the 
tail  water  is  discharged  into  the  excavated  river  bed  beneath  the 
power  houses.  Power  House  No.  i  is  designed  to  develop  6,000 
h,  p.  is  six  units,  and  No.  2  about  3,000  h.  p.  mainly  in  two  units. 


Fig.  336. — Plant  of  Columbus  (Ga.)   Power  Co.     Double  Horizontal  Turbines 
in  Open  Penstock.     (Engineering  News.) 


Power  house  No.  i  is  137  feet  long  and  52  feet  wide.  It  rests  on 
heavy  stone  foundations,  the  up-stream  portions  of  which  form  the 
heavy  bulk-head  which  is  pierced  by  six  large  openings  for  plant  No. 
i,  by  a  smaller  opening  for  the  exciter  units  and  a  larger  one  for 
the  penstock  leading  to  power  house  No.  2. 

The  openings  for  power  house  No.  I  are  short  flumes  or  chambers. 
The  back  end  of  each  of  the  wheel  chambers  is  closed  with  a 
heavy  plate  or  bulkhead  of  cast  iron  and  steel  separating  the  wheel 
chamber  from  the  generator  room.  The  racks  are  of  the  usual  con- 


548  Examples  of  Water  Power  Plants. 

struction  and  are  supported  on  a  framework  of  I-beams,  giving 
them  an  inclination  of  about  12°  with  the  vertical.  The  gates  to  the 
wheel  chambers  are  of  timber  and  are  raised  by  hand  by  means  of  a 
rack  and  pinion. 

Each  of  the  main  wheel  chambers  contains  a  pair  of  horizontal 
39  inch  Hercules  turbines,  which  discharge  into  a  common  draft 
tube.  The  center  line  of  the  wheels  is  15  feet  below  normal  head 
water  level  and  25  feet  above  normal  tail  water  level.  Under  the 
total  head  of  40  feet,  each  pair  of  wheels  develops  1,484  h.  p.  at  200 
r.  p.  m.  The  draft  tubes  are  7%  feet  in  diameter  at  the  turbine  cas- 
ing and  10  feet  at  the  discharge  end. 

Each  pair  of  wheels  is  direct  connected  to  a  two-phase  alternator 
built  by  the  Stanley  Electric  Manufacturing  Company.  Each  ma- 
chine has  a  rated  capacity  of  1,080  k.  w.  at  6,000  volts  and  driven  at 
200  r.  p.  m.  gives  current  at  60  cycles.  Each  is  connected  to  the 
wheel  shaft  by  a  flexible  leather  coupling. 

There  are  two  exciters  directly  connected  to  a  single  18  inch 
Hercules  wheel.  Each  exciter  is  of  the  Eddy  type,  having  a  capac- 
ity of  60  k.  w.  at  75  volts  and  running  at  450  r.  p.  m.  The  exciters 
are  under  the  control  of  mechanical  governors-* 

278.  Plant  of  The  Dolgeville  Electric  Light  and  Power  Co. — In 
Fig.  337  is  shown  the  plant  of  The  Dolgeville  Electric  Light  and 
Power  Company  at  High  Falls,  New  York,  on  what  is  now  known 
as  the  Auskerada  River. 

The  dam  is  built  of  limestone  masonry.  The  height  at  the  spill- 
way is  20  feet,  with  each  abutment  6  feet  higher.  The  total  length 
is  about  195  feet.  The  width  at  the  top  is  7  feet  and  at  the  boittom 
26  feet.  The  upstream  side  is  perpendicular,  the  downstream  side 
being  curved  in  order  to  properly  receive  and  discharge  the  water. 
The  head  gate,  12  ft.  square  and  built  in  two  sections,  is  fitted  with 
a  by-pass  gate  to  relieve  the  pressure  when  filling  the  flume.  The 
steel  flume  extends  from  the  head  gate  to  the  power  house,  520  feet 
away.  This  flume  is  10  feet  in  diameter,  and  is  made  of  %  mcn 
steel  plate,  all  longitudinal  seams  being  double  riveted.  Just  out- 
side the  dam  is  a  vent  pipe  which  assists  in  relieving  the  flume 
from  any  sudden  strains. 

There  are  two  36  inch  horizontal  Victor  turbines,  each  direct 
connected  to  one  450  k.  w.  2,400  volt  two-phase  Westinghouse  gen- 

*  See  Electrical  World  and  Engineer,  Jan.  23,  1904  or  Eng.  Record,  Jan.  16, 
1904. 


Plant  of  Dolgeville  Electric  Light  and  Power  Co.         549 


550  Examples  of  Water  Power  Plants. 

erator.  Each  of  these  wheels  will  develop  600  h.  p.  at  300  r.  p.  m., 
under  the  working  head  of  the  water,  which  is  72  feet.  They  are 
mounted  in  cylindrical  steel  casings,  and  discharge  downward 
through  draft  tubes,  which  extend  a  few  inches  below  the  sur- 
face of  the  tail  water.  Each  wheel  is  supplied  with  a  Giesler  elec- 
tromechanical governor.* 

279.  Plant  of  the  Shawinigan  Water  and  Power  Company. — The 
power  plant  of  the  Shawinigan  Water  and  Power  Company  is  lo- 
cated on  the  St.  Maurice  River,  Canada,  at  a  point  about  21  miles 
from  Three  Rivers,  90  miles  from  Quebec,  and  84  miles  from  Mon- 
treal station.  Fig.  338  shows  a  cross-section  of  their  power  station. 

The  St.  Maurice  River  has  a  total  length  of  over  400  miles,  and  is 
supplied  from  a  great  many  lakes  and  streams,  the  drainage  area 
being  about  18,000  square  miles.  The  water  flow  is  very  steady 
throughout  the  year  on  account  of  the  dense  forest  covering  this 
area,  and  is  in  the  neighborhood  of  26,000  cu.  ft.  per  second,  seldom 
going  below  20,000  cu.  ft.  per  second.  At  the  crest  of  the  falls  the 
water  flows  over  a  natural  rock  dam  and  then  down  over  the  cas- 
cade, making  a  fall  of  about  100  feet,  then  on  in  a  narrow  gorge 
through  which  the  water  rushes  swiftly  and  in  which  there  is  a 
further  fall  of  50  feet. 

The  intake  canal  is  1,000  ft.  long,  100  ft.  wide  and  20  ft.  deep.  Its 
entrance  from  the  river  is  located  in  a  rather  rapidly  flowing  stream 
at  the  crest  of  the  falls  where  the  water  is  20  feet  deep,  for  the  reason 
that  at  times  of  rather  high  water,  when  the  ice  is  flowing  out  of  the 
river,  the  current  is  expected  to  carry  the  ice  past  the  mouth  of  the 
canal.  The  end  of  the  canal  where  it  comes  out  at  the  face  of  the 
hill  is  closed  by  a  concrete  wall  from  which  the  water  is  led  through 
steel  penstock  pipes  down  to  the  power  house  130  feet  below. 
The  concrete  wall  or  bulkhead  in  the  canal  is  40  feet  in  height, 
about  30  feet  in  thickness  at  the  bottom  and  12  feet  at  the  top. 
On  top  of  this  wall  are  set  hydraulic  cylinders  for  lifting  the  head- 
gates  and  on  top,  covering  the  cylinders,  is  a  brick  gate  house-  The 
steel  penstocks  are  9  feet  in  diameter. 

The  electrical  apparatus  was  supplied  by  the  Westinghouse  Elec- 
tric &  Manufacturing  Company  and  the  turbines  by  the  I.  P.  Morris 
Co. 

The  three  turbine  units  of  the  original  installation  are  horizontal 
double  units  of  6,000  h.  p.  These  are  direct  connected  with  single 

*See  American  Electrician,  April,  1898,  Vol.  10,  No.  4. 


Plant  of  the  Shawnigan  Water  Power  Co. 


552  Examples  of  Water  Power  Plants. 

5,000  h.  p.  generator  units  of  the  rotating  field  type,  with  twenty 
poles.  They  are  designed  to  operate  at  180  r.  p.  m.  giving  two-phase 
currents  at  30  cycles  per'  second  and  2,200  volts.  A  later  installa- 


Fig.  339.— Plant  of  Concord  Electric  Co.     Sewall's  Falls  Plant.     Vertical  Tur- 
bines Connected  in  Tandem.     (Engineering  Record.) 

tion  consists  of  two  10,000  h.  p.  water  wheels  each  driving  a  6,600 
"k.  w.  generator.     (See  Figs.  159  and  236.) 

A  separate  penstock  is  provided  for  the  exciter  units  which  con- 
sist of  two  400  h.  p.  turbines  direct  connected  to  exciters.* 


*  See  references  as  given:  Eng.  Rec.  Apr.  28,  1900;  Can.  Engr.,  Ap-r.  1901, 
May,  1901,  and  May,  1902;  El.  Wld.  and  Engr.,  Feb.  8,  1902;  Cassier's  Mag., 
June,  1904. 


Plant  of  the  Concord  Electric  Company.  553, 

280-  Plant  of  the  Concord  Electric  Company. — This  plant,  shown 
in  Fig.  339,  is  situated  at  Sewall's  Falls  on  the  Merrimac 
River  about  four  miles  from  the  State  House  in  Concord,  New 
Hampshire.  The  dam  is  a  timber  crib-work  structure  about  500' 
long  and  gives  a  fall  varying  from  16'  to  17'.  The  addition  to  the 
old  plant  is  the  one  shown  in  cross-section  by  Fig.  339  and  is  of 
special  interest  due  to  the  vertical  shaft  generating  units  which 
were  here  installed.  Comparative  estimates  showed  that  all  other 
features  of  the  plant,  except  the  machinery  could  be  built  cheaper 
with  the  vertical  shaft  installation  and  the  machinery  added  only 
a  few  thousand  dollars  to  the  total  cost,  while  other  advantages  de- 
ermined  its  installation.  / 

The  new  installation  consists  of  two  units,  each  consisting  of 
3 — 55"  bronze  runners  of  the  Francis  type,  mounted  on  a  vertical 
shaft  and  hung  on  a  step  bearing.  The  machines  are  of  the  Escher- 
Wyss  type  built  by  The  Allis  Chalmers  Company,  American  rep- 
resentatives of  the  Escher:Wyss  Co.  The  gates  are  of  wicket  pat- 
tern, controlled  by  Escher-Wyss  mechanical  governors,  also  built 
by  The  Allis  Chalmers  Company.  The  generators,  which  are  direct 
connected  to  the  vertical  shaft  wheels,  are  of  500  k.  w.,  3-phase, 
60  cycle,  2,000  volt,  100  r.  p.  m.,  revolving  field  type.  Excitation  is 
furnished  by  one  75  h.  p.,  3-phase,  2,600  volt  induction  motor,  direct 
connected  to  a  45  k.  w.,  125  volt,  compound  wound  D.  C.  generator. 
The  exciter  unit  runs  at  680  r.  p.  m.* 

281.  Plant  of  Winnipeg  Electric  Railway  Co. — In  Fig.  340  is 
shown  the  power  plant  of  the  Winnipeg  Electric  Railway  Company. 
It  is  situated  on  the  Winnipeg  River  at  a  point  a  few  miles  from 
Lac  du  Bonnet,  which  is  on  a  branch  line  of  the  Canadian  Pacific 
Railroad,  65  miles  distant  from  the  City  of  Winnipeg. 

To  obtain  the  necessary  water,  a  canal  120  feet  wide  and  with  a 
clear  depth  of  8  feet  at  normal  low  water  was  cut  to  the  upper  river 
near  Otter  Falls.  The  canal  is  8  miles  long,  with  a  drop  of  5  feet 
to  the  mile,  equaling  a  total  head  of  40  feet.  At  the  point  where  the 
dam  is  located  there  is  a  natural  fall,  and  the  dam  crosses  almost  at 
the  crest. 

With  the  head  and  discharge  available  it  is  claimed  that  30,000 
electrical  horse  power  can  be  developed. 

The  water  wheels  are  all  McCormick  turbines  regulated  by  Lorn- 
bard  governors.  The  turbine  pits  are  protected  by  racks  to  keep 
out  ice,  logs,  etc. 

*See  Engineering  Record,  January  6th,  1906. 


554 


Examples  of  Water  Power  Plants. 


Plant  of  Nevada  Power  Mining  and  Milling  Co. 


555 


The  electrical  units  consist  of  four  1,000  k.  w.  and  five  2,000  k.  w. 
revolving  field,  60  cycle,  2,300  volt,  three-phase  generators  and  two 
100  k.  w.  125  volt,  direct-current  exciters,  all  coupled  to  turbines, 
and  two  175  k.  w.  125  volt  direct-current  exciters,  coupled  to  three- 
phase,  2,300  volt  induction  motors. 

There  are  15  transformers,  comprising  five  banks,  by  means  of 
which  the  voltage  "is  stepped  up  from  2,300  to  60,000  volts  for  trans- 
mission to  the  sub-station  at  Winnipeg  over  a  distance  of  65  miles.* 


Fig.  341 — Plant  of  Nevada  Power  Mining  and  Milling  Co. 
(Engineering  Record.) 

282.  Plant  of  Nevada  Power  Mining  and  Milling  Co. — Fig.  341 
shows  a  section  through  the  plant  of  The  Nevada  Power  Mining 
and  Milling  Company  on  Bishop  Creek,  near  Bishop,  Cal.  The 
equipment  of  the  station  consists  of  two  750  k.  w.,  60  cycle,  2,200 
volt,  three-phase  alternating-current  generators,  running  at  450 
r.  p.  m.  and  a  1,500  k.  w.  generator  running  at  400  r.  p.  m.  This 
latter  generator  is  shown  in  the  sectional  drawing.  There  are  two 
exciters  of  60  k.  w.  each,  delivering  current  at  140  volts  pressure. 
Both  exciters  are  operated  by  water  wheels,  and,  in  addition,  one  is 
provided  with  an  induction  motor.  The  water  wheels  were  made 
by  The  Pelton  Water  Wheel  Company  of  San  Francisco.  The  two 

*  See  Electrical  World,  June  23,  1906. 


556  Examples  of  Water  Power  Plants. 

750  k.  w.  machines  have  Sturgess  governors,  and  the  1,500  k.  w. 
machine  has  a  type  Q  Lombard  governor.  Hand-control  mechan- 
ism is  provided  for  each  wheel.  Oil  is  supplied  to  the  governor  by 
two  oil  pumps  operated  by  water  wheels. 

Water  is  taken  from  the  creek  at  a  small  diverting  dam  and  con- 
veyed along  the  mountain-side  in  a  pipe  line.  The  pipe  line  is  about 
12,000  feet  long,  and  consists  of  6,700  feet  of  42-inch  wood-stave 
pipe,  2,150  feet  of  3O-inch  wood-stave  pipe,  and  3,150  feet  of  24-inch 
steel  pipe,  all  diameters  being  inside  measurements.  The  42-inch 
pipe  lies  on  a  nearly  level  grade,  the  static  head  at  the  lower  end 
being  about  30  feet.  At  this  point  are  placed  two  3o-inch  gate 
valves,  one  opening  into  the  3O-inch  pipe  and  the  other  provided  for 
a  future  line.  The  3O-inch  pipe  descends  the  hill  to  a  point  that 
gives  a  static  head  of  265  feet.  Here  it  joins  the  24-inch  steel  pipe, 
which  descends  a  steep  hill  to  the  power  house,  the  total  static 
head  being  1,068  feet. 

The  power  generated  at  the  plant  is  transmitted,  over  a  line  of 
stranded  aluminum,  equivalent  to  No.  o  copper,  to  Tonopah  and 
Goldfield,  Nev.,  making  a  total  length  of  line  of  113  miles.  In 
crossing  the  White  Mountains  the  line  reaches  an  elevation  of  over 
10,500  feet.* 

LITERATURE. 

1.  Hydro-Electric  Development  at  North  Mountain,  Cal.     Elec.  World  and 

Engineer,  March  4,  1905. 

2.  The  Northern  California  Power  Company's  Systems.    Electrical  World  and 

Engineer,  Sept.  10,  1904. 

3.  The  Power  Plants  of  the  Edison  Electric  Company  of  Los  Angeles.    Eng- 

ineering Record,  March  18,  1905. 

4.  The  Fresno  Transmission  Plant.     The  Journal  of  Electricity,  April,  1896. 

5.  The  Edison  Company's  System  in  Southern  California.    Electrical  World 

and  Engineer,  March  11,  1905. 

6.  An  83-Mile  Electric  Power  Transmission  Plant,  Cal.     Cassier's  Magazine, 

November,  1899. 

7.  Bishop  Creek,  Cal.     Hydro-Electric  Power  Plant.     Electrical  World,  June 

30,  1906. 

8.  The  Hydraulic  Power  Development  of  the  Animas  Power  and  Water  Com- 

pany.    April   14,   1906,   Enginering   Record.     Electrical   Review, 
Jan.  30,  1904.     Engineering  News,  Jan.  4,  1906. 

9.  Power  Transmission  in  Pike's  Peak  Region.     Electrical  World  and  Eng- 

ineer, July  26,  1902.     Electrical  World,  May  26,  1906.     Engineer- 
ing Record,  May  19,  1906.     Engineering  Record,  July  19,  1902. 


*  See  Engineering  Record,  June  30,  1906,  or  Electrical  World  of  June  30, 
1906. 


Literature.  557 

10.  New  Water  Power  Development  at  New  Milford,  Conn.     Engineering  Rec- 

ord, Feb.  13,  1904. 

11.  Berkshire  Power  Company,  Canaan,  Conn.  Electrical  Review,  Sept  7,  1907. 

12.  Plant  of  Hartford  Electric  Light  Company.     American  Electrician,  March 

1900. 

IS.Hydro-Electric  Power  Plant  and  Transmission  Lines  of  the  North  Georgia 
Electric  Company.     Electrical  Review,  Oct.  20,  1906. 

14.  Atlanta  Water  and  Electric  Power  Company's  plant  at  Morgan  Falls,  Ga. 

Engineering  Record,  Apr.  23,  1904. 

15.  Plant  of  The  South  Bend  Electric  Company,  South  Bend,  Ind.    Electrical 

World  and  Engineer,  May  30,  1903. 

16.  Plant  at  Rock  Island  Arsenal,  Rock  Island,  111.    Western  Electrician,  Nov. 

23,  1901. 

17.  The  Hydraulic  Development  of  the  Sterling  Hydraulic  Company.     Engin- 

eering Record,  Dec.  16,  1905. 

18.  Joliet  Water  Power  of  Chicago  Drainage  Canal.     Engineering  Record, 

Apr.  19,  1902. 

19.  Development  of  Electric  Power  at  Shoshone  Falls,  Idaho.    Western  Elec- 

trician, Mar.  9,  1907. 

20.  Chaudiere  Falls  Power  Transmission  Company,  Maine.     Electrical  World 

and  Engineer,  June  15,  1901.     Engineering  News,  May  7,  1903. 

21.  Water  Power  at  Portland,  Me.    Electrical  World  and  Engineer,  Jan.  10, 

1903. 

22.  Plant  at  Deer  Rips,  Me.    Electrical  World  and  Engineer,  Apr.  8,  1905. 

23.  Great  Northern  Paper  Company's  New  Mill,  Me.     Engineering  Record, 

Dec.  15,  1900. 

24.  A  Submerged  Power  Station,  Md.     Engineering  Record,  Aug.  24,  1907. 

25.  High  Pressure  Power  on  the  Housantonic,  Mass.     Electrical  World  and 

Engineer,  Feb.  13,  1904. 

26.  Development  at  Turner's  Falls,  Mass.     Electrical  World  and  Engineer, 

Aug.  12,  1905. 

27.  Power  on  the  Blackstone  River,  Mass.     Electrical  World  and  Engineer, 

Oct.  14,  1905. 

28.  New   Plant   of   Holyoke   Water   Power   Company.     Engineering   Record, 

Sept.  15,  1906. 

29.  Lowhead  Hydro-Electric  Developments  in  Michigan.     Engineering  Record, 

Oct.  19,  1907. 

30.  Plant  of  the  Michigan-Lake  Superior  Power  Company,  Sault  Ste.  Marie. 

American  Electrician,  August,   1898.     Engineering  News,   Sept. 
25,  1902.     Electrical  World  and  Engineer,  Nov.  8,  1902. 

31.  Transmission  Plant  of  Kalamazoo  Valley  Electric  Company,  Mich.    Am- 

erican Electrician,  July,  1901. 

32.  Water  Power  Development  at  Little  Falls,  Minn.,  and  Its  Industrial  Re- 

sults.    Engineering  Record,  June  13,  1905. 

33.  St.  Anthony  Falls  Water  Power  Plant,  Minn.    American  Electrician,  May, 

1898. 

34 


558  Examples  of  Water  Power  Plants. 

34.  Great   Northern   Power   Company   of   Duluth,   Minn.     Electrical    World, 

July  28,  1906. 

35.  Electric  Power  Transmission  Plant,  Butte,  Mont.    American  Electrician, 

February,  1898. 

36.  Generating  System  of  The  Portland  General  Electric  Company.     Engineer- 

ing Record,  Aug.  12,  1905. 

37.  The  Water  Power  Plant  at  Hannawa  Falls,  N.  Y.     Engineering  Record, 

Dec.  7,  1901. 

38.  The  Water  Power  Development  at  Massena,  N.  Y.    Power,  December,  1900. 

39.  Hudson   River   Power   Plant   at  Mechanicville,   N.   Y.     American   Elec- 

trician, September,  1898.    Engineering  News,  Sept.  1,  1898.    Elec- 
trical World,  Nov.  13,  1897. 

40.  Hudson  River  Power  Plant  at  Spier  Falls,  N.  Y.    Engineering  Record, 

June  27,  1903.     Electrical  Review,  July  21,  1906. 

41.  Hydraulic  Developments  at  Trenton  Falls,  N.  Y.     Electrical  World,  May 

19,  1906. 

42.  Station  of  Rochester  Gas  and  Electric  Company.     Electrical  World  and 

Engineer,  Nov.  13,  1903. 

43.  New   Hydro-Electric   Power   Plant  of   Cornell   University.     Engineering 

Record,  May  20,  1905. 

44.  Hydro-Electric  Developments  in  the  Adirondacks.     Electrical  World,  Apr. 

26,  1906. 

45.  Hydraulic  Development,  Middletown,  N.  Y.    Electrical  World  and  Eng- 

ineer, Aug.  8,  1903. 

46.  Niagara  Falls  Power  Developments.     Cassier's  Magazine  (Niagara  Power 

number).    Engineering  News,  1901,  vol.  1,  p.  71. 

47.  Power  Plants  of  The  Portland  Railway  Light  and  Power  Company,  Port- 

land, Ore.     Engineering  News,  June   27,   1907.     Engineer,   Apr. 
15,  1907. 

48.  Garvin's  Falls  Plant,  Manchester,  N.  H.     Engineering  Record,  Jan.  24, 

1903.  Engineering  News,  March  19,  1903.     Electrical  World  and 
Engineer,  May  28,  1904. 

49.  Concord,  N.  H.  Water  Power.   Electrical  World  and  Engineer,  July  12, 1902. 

50.  Plant  at  Sewall's  Falls,  N.  H.     Engineering  Record,  Jan.  5,  1906. 

51.  Water  Power  at  Manchester,  N.  H.    Electrical  World  and  Engineer,  Jan. 

17,  1903. 

52.  York  Haven,  Pa.  Transmission  Plant.    Electrical  World  and  Engineer, 

Sept.  19,  1903.     Electrical  World,  March  2,  1907. 

53.  Developments  at  Huntingdon,  Pa.    Electrical  World  and  Engineer,  Dec. 

22,  1906. 

54.  Hydro-Electric  Plant  of  the  McCall-Ferry  Power  Company,  Pa.    Engineer- 

ing Record,  Sept.  21,  1907.     Electrical  Review,  June  1,  1907. 

55.  The  Warriors  Ridge  Hydro-Electric  Plant  at  Huntingdon,  Pa.     Engineer- 

ing Record,  Dec.  22,  1906. 

56.  Hydro-Electric   Developments   on   the    Catawba   River,    South    Carolina. 

Electrical  World,  May  25,  1907.    Engineering  Record,  July  30, 

1904.  Electrical  World  and  Engineer,  July  23,  1904. 


Literature  559 

57.  Construction  of  the  Neals  Shoals  Power  Plant  on  Broad  River,  S.  C.     Eng- 

ineering Record,  March  3,  1906. 

58.  A  Large  Hydraulic  Plant  at  Columbia,  S.  C.     The  Engineering  Record, 

Jan.  1,  1898. 

59.  Greenville-Carolina  Power   Company,   S.  C.     Electrical   World,   June   22, 

1907. 

60.  Water  and  Electric  Power  Plant  of  the  Utah  Sugar  Company.     Engineer- 

ing News,  Apr.  13,  1905. 

61.  Bear  River  Power  Plant  and  Utah  Transmission   Systems.     Electrical 

World  and  E'ngineer,  June  18,  1894. 

62.  Plant  of  the  Chittenden  Power  Company,  Rutland,  Vt.     Engineering  Rec- 

ord, Dec.  9,  1905. 

63.  Plant  of  Vermont  Marble  Company,  Proctor,  Vt.     Electrical  World,  Feb. 

3,  1906. 

64.  Water  Wheel  Equipment  in  the  Puget  Sound  Power  Company's  Plant. 

Electrical  World  and  Engineer,  Oct.  22,  1904. 

65.  Hydraulic  Power  Plant  on  the  Puyallup  River,  near  Tacoma.     Engineer- 

ing Record,  Oct.  1,  1904.  Engineering  News,  Sept.  29,  1904. 
Electrical  World  and  Engineer,  Oct.  1,  1904. 

66.  Snoqualmie  Falls  Water  .Power  Plant  and  Transmission  System.     Eng- 

ineering News,  Dec.  13,  1900.  Western  Electrician,  Aug.  20,  1898. 
Electrical  World  and  Engineer,  May  7,  1904. 

67.  Apple  River  Power  Plant,  Wisconsin.     Electrical  World  and  Engineer, 

Dec.  8,  1900. 

68.  St.  Croix  Power  Company,  Wisconsin.     American  Institute  of  Electrical 

Engineers,  1900.  Engineering  Record,  March  3,  1906.  Western 
Electrician,  Oct.  27,  1906. 

69.  The  Lachine  Rapids  Power  Plant,  Montreal,  P.  Q.     Engineering  News, 

Feb.  18,  1897. 

70.  Shawinigan   Falls   Electrical   Development.     Electrical  World  and  Eng- 

ineer, Feb.  1,  1902.  Cassier's  Magazine,  June,  1904.  Engineer- 
ing Record,  April  28,  1900.  Canadian  Engineer,  April  and  May, 
1901  and  May,  1902. 

71.  60,000-volt  Hydro-Electric  Plant,  Winnipeg,  Manitoba.     Electrical  World, 

June  23,  1906. 

72.  DeCew  Falls  Power  Plant.     Engineer,  Apr.  2,  1906. 

73.  Development  of  the  Montmorency  Falls.     Electrical  World  and  Engineer, 

June  17,  1899. 

74.  The  Rheinfelder  Power  Transmission.     Electrician,  March  26,  1897. 

75.  The  Bellinzona,  Italy,  Hydro-Electric  Station.     Electrical  World  and  Eng- 

ineer, Sept.  16,  1905. 

76.  A  Norwegian  Water  Power  Plant.     Electrical  World  and  Engineer,  Apr. 

4,  1903. 

77.  An  Italian  40,000-volt  Transmission  Plant.     Electrical  World  and  Eng- 

ineer, Aug.  19,  1905. 

78.  Tyrol  Hydro-Electric  Power  Station,  Keiserwerke.   Electrical  World,  May 

11,  1907. 


560  Examples  of  Water  Power  Plants. 

79.  The  Rome-Tivoli  Electric  Installation.     Cassier's  Magazine,  March,  1899. 

80.  The  Tusciano  Hydro-Electric  Power  Station.     The  Engineer,  July  16,  1906. 

81.  Hydraulic  Station  at  Gusset,  near  Lyons,  France.     Electrical  World  and 

Engineer,  Dec.  9,  1905. 

82.  Hydro-Electric  Plant  of  the  City  of  Drammen,  Norway.     Electrical  Re- 

view, March  31,  1908. 

83.  The  First  British  Hydro-Electric  Power  Transmission.    Electrical  World, 

vol.  47,  p.  108. 

84.  The  Hydro-Electric  Sation  at  Bogota.     Engineering  Record,  Sept.  3,  1904. 

85.  The  Sill  Hydraulic  Power  Plant  near  Innsbruck.     July  1,  1905. 

86.  The  Electric  Power  and  Transmission  System  of  Schaffhausen,  Switzer- 

land.    Electrical  World  and  Engineer,  March  19,  1904. 

87.  A  Bohemian  Hydro-Electric  Plant.    Electrical  World,  July  21,  1906. 

88.  Hydro-Electric  Power  Installation  in  lyo,  Japan.     Electrical  World  and 

Engineer,  July  9,  1904. 

89.  Electric  Power  at  Jajce,  in  Bosnia.     Cassier's  Magazine,  October,  1901. 

90.  26,000-volt  Installation  at  Grenoble,  France.     Electrical  World  and  Eng- 

ineer, Jan.  31,  1903. 

91.  An  Unusual  Water  Power  Plant  at  Kykkelsind,  Norway.     Engineering 

Record,  July  2,  1904. 

92.  The  Hydro-Electric  Plant  at  Lucerne,   Switzerland.     Electrical  Review, 

Aug.  11,  1906. 

93.  The  Guanajuato,  Mexico,  Power  Transmission.  Electrical  World  and  Eng- 

ineer, Aug.  6,  1904. 


CHAPTER  XXIII. 

THE  RELATION  OF  DAM  AND  POWER  STATION. 

283.  General  Consideration. — In  any  water  power  plant  the 
water  must  be  taken  from  some  source,  conducted  to  the  wheels, 
and  discharged  from  the  same  at  the  lower  head.  To  accomplish 
this  object  there  must  be  a  head-race  leading  from  the  source  of 
supply  to  the  plant  which  may  be  of  greater  or  less  length  and  in 
which  more  or  less  of  the  available  head  may  be  lost  in  order  to 
produce  the  velocity  of  flow  and  overcome  the  frictional  resistance. 


Fig.  342. 

After  entering  the  plant  the.  water  is  discharged  through  the 
turbine  T  into  a  tail-race  of  greater  or  less  extent  in  which  there 
is  also  a  loss  caused  by  friction  and  velocity  of  flow,  similar  to  that 
already  expended  in  the  head-race.  In  Fig.  342  the  total  head 
available  is  H;  the  head  lost  in  the  head-race  is  indicated  by  h± ; 
and  the  head  lost  in  the  tail-race  is  indicated  by  h2.  The  net  energy 
of  the  wheel  is  h  =  H  —  hx — hs,  and  a  portion  of  h  is  also  lost  in 
the  slip,  leakage,  and  friction  of  the  machinery  and  transmission- 

The  power  plant  should  be  located  with  reference  to  the  dam 
so  that  (i)  the  greatest  amount  of  head  may  be  utilized  at  the  least 
expense :  (2)  the  plant  constructed  should  be  as  free  as  possible 
from  interruptions  due  to  floods  or  other  contingencies ;  (3)  the 
location  chosen  should  be  at  such  a  point  where  security  of  con- 
struction can  be  accomplished  at  the  minimum  expense. 

Each  of  these  influences  is  of  importance  and  the  relative  location 
of  the  power  plant  and  dam  must  depend  upon  these  and  various 
other  conditions  which  must  be  carefully  considered. 


562  The  Relation  of  Dam  and  Power  Station. 

284.  Classification  of  Types  of  Development.— For  the  purpose 
of  a  clear  understanding  of  the  principles  involved,  the  type  of 
development  may  be  grouped  or  classified  into : 

First :  Concentrated  fall,  in  which  the  plant  is  built  on  the  dam 
or  closely  adjoining  thereto,  with  a  short  or  no  race.  In  this  case 
the  entire  fall  is  concentrated  by  means  of  the  dam  and  as  a  rule 
this  class  of  development  is  adaptable  only  to  central  power  sta- 
tions where  one  or  two  plants  only  are  to  be  installed  on  the 
power. 

Second:  Diversion  type  with  dam.  In  this  case  the  fall  is  de- 
veloped by  means  of  a  dam  in  the  manner  conforming  to  the  last 
type  but  the  water  is  distributed  to  one  or  more  plants  by  means 
of  a  long  head-race  canal  through  which  the  water  flows  to  the 
power  station,  after  which  it  is  discharged  either  into  the  stream 
at  some  point  below  the  dam  or  into  a  tail-race  from  which  it  is 
finally  discharged  at  a  point  lower  down  the  stream. 

Third:  Diversion  with  or  without  dam.  In  this  case  the  develop- 
ment is  installed  with  or  without  a  dam  at  the  head  of  the  rapids 
or  fall  which  is  to  be  utilized  and  the  water  is  conducted  through 
a  long  head  race,  if  land  of  a  suitable  elevation  is  available,  or>, 
otherwise,  through  a  tunnel  to  a  point  immediately  above  the  site 
of  the  power  station.  From  the  end  of  the  tail-race  or  tunnel  the 
water  is  carried  to  the  plant  through  a  metallic  penstock. 

Fourth :  The  fourth  type  is  similar  to  the  third  except  that  where 
the  head-race  or  tunnel  is  used  (the  ground  being  unfavorable  to 
such  construction  or  the  expense  of  the  same  being  unwarranted) 
a  long  penstock  of  metal  is  provided  to  conduct  tlie  water  from 
the  head  works  to  the  station. 

Fifth  :  The  fifth  type  is  the  tunnel  tail-race  type  and  involves  con- 
ducting the  water  through  metallic  penstock  direct  to  the  wheels 
located  at  the  minimum  level  and,  after  the  water  is  discharged 
therefrom,  the  provison  of  a  tunnel  tail-race  for  conducting  the 
water  from  the  turbine  to  the  point  where  it  is  to  be  discharged 
back  into  the  stream. 

It  is  important  to  note  in  this  case,  as  in  the  case  of  all  other 
classifications  attempted,  that  such  a  classification  is  for  the  pur- 
pose of  systematizing  the  consideration  of  numerous  diversified 
types  and  bringing  them  to  a  similar  basis  for  examination.  In 
the  actual  adaptation  of  plans  of  development,  it  is  seldom  any  sin- 
gle type  will  be  found  in  its  simplicity ;  in  most  cases  modifications 
of  the  same  become  desirable  or  essential. 


Classification  of  Types  of  Development. 


563 


Fig.  343. 


564  The  Relation  of  Dam  and  Power  Station. 

285.  Concentrated  Fall. — In  most  of  the  low  head  water  powers 
the  portion  of  the  fall  of  the  river  which  can  be  utilized  is  distrib- 
uted over  minor  rapids  and  small  falls  and  occupies  a  considerable 
length  of  the  stream.    Where  the  head  is  small  and  the  expense  of 
a  dam  to  concentrate  the  head  entirely  at  one  point  is  permissible, 
the  power  house  may  sometimes  be  located  to  advantage  in  the  dam 
itself.     In  this  case  the  power  house  will  constitute  a  part  of  the 
dam  itself.    This  is  possible  only  where  the  length  of  the  spillway 
remaining  is  sufficient  to  pass  maximum  flood  without  an  undue 
rise  in  the  head  of  the  water  .above  the  dam.    In  many  such  cases 
this  plan,  which  is  represented  by  Diagram   C,   Fig.  343,  meets 
economical  construction  as  it  may  both  cheapen  the  cost  of  the 
dam  and  reduce  the  excavation  necessary  for  the  wheel  pit  and  tail- 
race.     The  power  house  built  at  such  point  is,  however,  usually 
directly  in  the  line  of  the  current  and  must  be  so  constructed  and 
protected  as  to  prevent  its  injury  or  destruction  by  floods,  ice  or 
other  contingencies  of  river  flow. 

In  other  cases,  where  the  spillway  available  by  the  above  plan  is 
not  sufficient  or  where  the  plant  is  not  properly  protected  by  such 
forms  of  construction,  the  plant  may  be  constructed  on  one  side 
of  the  dam,  receiving  its  waters  from  a  head-race  which  joins  the 
river  above  the  dam  and  discharges  it  into  the  river  below,  as 
shown  by  Diagrams  C  and  D,  Fig.  343.  Or,  where  the  capacity  is 
suitable,  the  plant  itself  may  receive  the  water  directly  from  its 
head  gate  from  the  river  above  the  dam  and  discharge  it  through 
a  tail-race  which  will  enter  the  river  at  some  point  below  the  dam, 
as  shown  in  Diagram  A,  Fig.  343. 

In  other  cases,  where  the  power  is  to  be  distributed  to  a  number 
of  independent  plants,  raceways  may  be  constructed  on  either  or 
both  sides  of  the  stream  and  from  the  dam,  following  the  stream 
downward  along  the  bank  and  more  or  less  approximately  parallel 
thereto  as  the  nature  of  the  conditions  demand.  The  plant  drawing 
the  water  from  this  head-race  may  be  distrbuted  at  various  points 
along  the  same,  and  from  these  plants  the  water  will  be  discharged 
after  use  either  directly  into  the  stream  itself  or  into  a  tail  race  con- 
necting such  plants  with  a  lower  point  farther  down  the  stream,  as 
shown  in  Diagram  E,  Fig.  343. 

286.  Divided    Fall. — An    independent    tail-race    is    usually    con- 
structed to  advantage  where  the  dam  concentrates  only  a  portion  of 
the  head  or  fall,  leaving  certain  additional  portions  to  be  developed 
by  the  use  of  the  tail-race,  which  may,  if  desirable,  enter  the  stream 


Classification  of  Types  of  Development, 


565 


Fig.  344. 


566  The  Relation  of  Dam  and  Power  Station. 

at  a  point  much  farther  down  the  river  and  at  the  foot  of  the  rapids. 
Where  the  fall  of  the  stream  is  considerable,  and  the  expense  of 
construction  of  the  dam  to  suitable  height  to  concentrate  the  entire 
fall  at  a  single  point  is  inadvisable,  it  is  often  desirable  to  build  a 
dam  to  less  height  at  perhaps  considerably  less  expense  and  develop 
at  the  dam  only  a  portion  of  the  total  fall.  From  this  dam  a  head- 
race may  extend  to  some  considerable  distance,  and  the  water  from 
this  head-race  may  be  delivered  to  the  power  plant  a  mile  or  two 
lower  down  the  stream.  From  this  head  race,  the  water,  after  pass- 
ing through  the  wheels,  is  carried  directly  into  the  stream  at  the 
lower  point,  as  shown  in  Diagram  G,  Fig.  344. 

Under  other  conditions,  where  the  topography  of  the  country  is 
suitable,  the  head-race  may  be  much  less  in  extent,  and  a  tail-race 
substituted  for  receiving  the  waters  after  they  have  been  used  in 
the  wheel  and  then  conducted  to  the  river  at  or  near  the  end  of  the 
rapids,  as  shown  in  Diagram  F,  Fig.  344. 

Under  still  other  conditions  the  plant  itself  may  be  located  imme- 
diately at  the  dam  and  the  tail  waters  may  be  conducted  from  the 
turbine  to  a  tail-race  or  tail-water  tunnel  to  the  lower  end  of  the 
rapids,  as  in  Diagram  H,  Fig.  344. 

The  relation  of  head-race  and  tail-race  is  merely  a  question  of 
developing  the  power  plant  at  the  least  cost  and  securing  the  max- 
imum head,  and  the  topographical  conditions  at  the  power  site  will 
therefore  determine  which  line  of  development  will  be  best.  In  a 
number  of  cases,  where  the  head  or  fall  is  considerable  and  the 
power  development  is  large,  and  where  the  cost  of  land  for  head- 
races would  be  almost  or  quite  prohibitive,  the  stations  have  been 
located  in  the  immediate  vicinity  of  the  river  and  have  delivered  the 
water  into  a  tail-race  tunnel,  which  frequently  empties  at  a  con- 
siderable distance  down  the  stream  and  at  the  lowest  point  of  deliv- 
ery that  is  practicable.  In  other  cases  it  is  more  economical  to  run 
open  raceways  for  a  portion  of  the  distance  and  then  conduct  the 
water  under  pressure  by  closed  pipes  to  the  wheels  at  the  lower 
point. 

This  last  method  is  used  particularly  under  high  head  and  where 
the  water  must  be  conducted  for  a  reasonable  distance  over  an  irreg- 
ular profile. 

The  quantity  of  water  to  be  used,  the  head  available,  and  the 
value  of  power  modify  the  arrangements  which  must  be  carefully 
studied  in  view  of  the  financial,  topographical,  and  other  modifying 
conditions. 


Distribution  of  Water  at  Various  Plants. 


287.  Examples  of  the  Distribution  of  Water  at  Various  Plants. — 
Fig.  345  is  a  plan  of  the  power  development  on  the  Rock  River  at 
Sterling,  Illinois.  The  dam  at  this  point  is  about  940  feet  in  length. 
The  power  is  owned  by  various  corporations  and  private  individuals 
who  have  combined  their  interests  in  the  dam  and  raceways  and 


ROCK 


Sterling  Hydraulic  Company. 


have  organized  The  Sterling  Hydraulic  Company,  whose  function 
is  to  maintain  the  same.  The  individual  plants  are  owned,  installed, 
and  operated  by  the  various  owners  or  by  manufacturers  who  lease 
the  power.  At  this  location  races  have  been  constructed  at  the  foot 
of  the  rapids,  but  these  rapids  continue  to  a  point  near  the  lower 
end  of  the  tail-race,  and  the  plants  farthest  from  the  dam  have  the 
highest  falls.  The  fall  varies  from  about  8  to  9%  feet. 


The  Relation  of  Dam  and  Power  Station. 


Fig.  346  shows  the  general  arrangement  of  the  canal  of  The  Hoi- 
yoke  Water  Power  Company  at  Holyoke,  Mass.  The  total  fall  of 
the  river  at  this  point,  from  the  head  water  above  the  dam  to  the 
tail  water  at  the  lowest  point  down  the  stream,  is  about  sixty  feet. 
The  fall  is  divided  into  three  levels  by  the  various  canals,  marked : 
ist  level  canal,  2nd  level  canal,  and  3rd  level  canal. 


Fig.  346. — Canals  of  Holyoke  Water  Power  Company. 

The  first  level  canal,  which  has  a  length  of  about  6,000  feet,  is  con- 
structed as  a  chord  across  the  bend  of  the  river  and  is  approximately 
some  3,000  feet  from  the  bend.  The  canal  is  about  150'  wide  near 
the  bulkhead  and  decreases  to  about  100'  at  the  lo>wer  end.  The 
water  depth  is  about  20'  at  the  upper  end  and  about  10'  at  the  lower. 
The  canals  are  all  walled  throughout  their  length  to  a  height  two  or 
three  feet  above  the  maximum  water  surface.  The  fall  from  the 
first  level  to  the  second  is  about  20'.  Various  mills  draw  their  water 
supply  from  the  first  level  as  a  head-race,  and  discharge  into  the 
second  canal  as  a  tail-race.  Near  the  upper  end  of  the  canal  are  a 
few  factories  that  draw  water  from  the  first  level  and  discharge  the 
same  into  the  river  with  a  head  of  some  35  or  40  feet. 

The  second  level  canal  is  built  parallel  to  the  first  and  at  a  dis- 
tance of  about  400  feet  nearer  the  river.  The  main  canal  is  about 
6,500  feet  in  length,  but  near  the  left  hand  of  the  map  is  shown  to 


Distribution  of  Water  at  Various  Plants. 


569 


Rear   devotion    of 

Fig.  347. — Kilboura  Plant  of  Southern  Wisconsin  Power  Co. 


57o 


The  Relation  of  Dam  and  Power  Station. 


sweep  round  towards  the  river  and  attain  a  reach  of  about  3,000 
feet  in  length  parallel  thereto.  The  mills  drawing  their  supply  from 
this  canal  discharge  either  directly  into  the  third  level  or  into  the 
river.  The  water  supply  from  each  of  the  lower  levels  is  the  tail 
water  from  the  next  level  above,  but  is  also  supplemented  by  over- 
flows when  the  mills  fed  from  the  level  above  are  not  discharging 


Fig.  348. — Plant  of  The  Lake  Superior  Power  Co. 

sufficient  water  to  maintain  the  quantity  needed  in  the  lower  level. 

The  fall  from  the  third  level  of  the  river  is  essentially  the  same 
for  all  the  mills  drawing  water  therefrom,  but  according  to  the  stage 
of  the  river  ranges  from  15  to  27  feet. 

The  flow  of  water  in  the  first  level  is  controlled  by  gates  and  its 
height  limited  by  an  overflow  of  about  200  feet  in  length  which 
acts  as  a  safety  overflow  and  prevents  any  great  rise  in  the  head 
water  during  times  of  flood. 

288.  Head-Races  Only. — Fig.  347  illustrates  the  general  plan  of 
the  hydraulic  power  development  of  The  Southern  Wisconsin  Power 
Company  at  Kilbourn,  Wisconsin.  Here  the  entire  cross-section  of 
the  stream  is  necessary  in  order  to  pass  the  maximum  volume  of 


Distribution  of  Water  at  Various  Plants. 


571 


572 


The  Relation  of  Dam  and  Power  Station, 


Distribution  of  Water  at  Various  Plants. 


573 


water,  which  amounts  to  about  80,000  second-feet.  The  plant  has 
therefore  been  constructed  at  one  side  of  the  river,  receives  the  flow 
through  a  series  of  gates  built  just  above  the  dam,  and  discharges 
the  water  into  the  river  just  below  the  bend  in  the  river,  as  shown. 
The  plant  now  under  construction  is  only  a  portion  of  that  which 
it  is  designed  to  ultimately  install.  The  proposed  future  extension 
of  the  power  plant  is  shown  by  the  dotted  lines. 


TWIN     FALLS 


Fig.  351. — Possible  Canal  for  Peshtigo  River  Development. 

Fig.  348  shows  the  water  power  plant  of  The  Lake  Superior 
Power  Company  at  St.  Mary's  Falls,  Michigan.  The  canal  on  the 
American  side  begins  just  above  the  entrance  to  the  American  ship 
canal  and  above  the  Soo  rapids.  The  water  is  conducted  through 
this  canal  to  a  power  house  located  below  the  rapids  at  the  point 
shown  on  the  map.  On  account  of  the  value  of  the  land  this  canal 
was  designed  for  a  velocity  of  flow  of  about  7%'  per  second  with 
full  load  of  the  plant,  which  was  designed  for  about  40,000  h.  p. 
requiring  a  capacity  with  available  head  of  16.2  feet,  of  about  4,200 
cubic  feet  per  second.  (See  Engineering  News  of  August  4th,  1898.) 
35 


574  The  Relation  of  Dam  and  Power  Station. 

Fig.  349  shows  the  plan  of  the  hydraulic  development  of  The 
Economy  Light  and  Power  Company  at  Joliet,  Illinois.  The  entire 
installation  as  shown  is  owned  by  this  company.  The  fall  available 
is  about  ii  feet  and  is  developed  by  a  concrete  dam  which  creates 
the  upper  basin  along  which  the  power  plant  has  been  constructed. 
The  water  flows  through  the  flume  gates  directly  on  to  the  wheels 
and  is  discharged  into  a  tail-race  built  parallel  with  the  river-  A 


49 


SO  51  52  S3  54  55 

MILES 

Fig.  352.— Profile  of  Peshtigo  River. 


certain  amount  of  water  is  necessary  for  feeding  the  lower  level  of 
the  canal  and  this  is  supplied  by  a  by-pass  tunnel  shown  in  dotted 
line  above  the  dam.  This  by-pass,  which  is  slightly  higher  than 
the  elevation  of  the  tail-race,  is  fed  by  the  discharge  of  one  of  the 
wheels,  which  operates  under  a  less  head  than  the  other  wheels  in 
the  installation. 

289.  Plant  Located  in  Dam. — In  Fig.  350  is  shown  the  general 
plan  and  elevation  of  the  hydraulic  plant  at  Dresden  Heights  on  the 
Des  Plaines  River  just  above  its.junction  with  the  Kankakee  River. 
These  two  streams  unite  at  this  point  to  form  the  Illinois  River. 

In  this  case  the  dam  is  built  across  a  very  wide  valley  and  the 
length  of  the  dam  is  much  greater  than  necessary  or  desirable  to 


High  Head  Developments. 


575 


\ 


S 


V, 


accommodate  the  flood  flow  of  the 
stream  which  is  approximately  25,000 
second-feet.  In  consequence,  the  pres- 
ent power  plant,  as  well  as  the  pro- 
posed extension  to  the  power  station, 
will  form  a  part  of  the  'dam  itself  and 
the  spillway  will  occupy  only  a  portion 
of  the  entire  length  of  the  structure 
and  is  so  designed  as  to  maintain  a  sat- 
isfactory head  at  times  of  flood  flow 
The  head  of  the  water  above  the  dam 
is  controlled  both  by  the  length  of 
spillway  and  by  six  tainter  gates  by 
means  of  which  the  level  of  the  water 
above  the  dam  can  be  controlled  at  all 
stages  of  flow. 

290.  High  Head  Developments.— 
Fig.  351  illustrates  the  general  plan  of 
a  possible  method  of  development  of 
the  Peshtigo  River  for  The  Northern 
Hydro-Electric  Company.  The  fall 
available  is  shown  by  the  profile, — Fig. 
352.  It  is  proposed  to  construct  a  dam 
above  High  Falls  of  sufficient  height 
to  back  the  water  over  Twin  Falls,  and 
to  either  develop  the.  power  at  High 
Falls  and  Johnson' s  Falls  independently 
or  conduct  the  water  by  a  canal  to  Mud 
Lake,  thence  to  Perch  Lake,  thence  to 
the  head  work  to  be  be  built  above 
Johnson's  Falls,  where  a  head  of  about 
110'  will  be  available.  If  a  single  de- 
velopment is  chosen  the  water  will  be 
be  conducted  from  the  head  works 
through  penstocks  to  the  power  plant 
to  be  built  at  the  base  of  the  bluff  below 
Johnson's  Falls.  The  canal  in  this  case 
will  conduct  the  head  waters  with  very 
little  fall  to  the  immediate  site  of  the 
plant,  thence  by  penstocks  to  the  tur- 
bine located  in  the  gorge  below. 


576 


The  Relation  of  Dam  and  Power  Station. 


Fig.  354,— Niagara  Falls  Power  Development. 


Head  Developments. 


577 


Fig.  353  is  a  plant  of  the  power  development  at  Trenton  Falls, 
New  York.  The  upper  portion  of  the  fall  is  developed  by  a  dam 
about  60'  in  height,  which  is  connected  by  an  84"  pipe  line  with  the 
turbine  located  in  the  power  house  about  two  miles  below.  The 
turbines  used  in  this  development  are  the  Fourneyron  turbines, 
which  are  described  in  Chap.  XIX,  and  are  illustrated  by  Fig.  311. 

Fig.  354  is  a  general  plan  of  the  water  power  developments  at 
Niagara  Falls.  The  first  development  was  that  of  The  Niagara 


Fig.  355. 

Falls  Hydraulic  and  Manufacturing  Company.  By  means  of  a 
canal  the  water  is  taken  from  the  upper  end  of  the  rapids  and  con- 
ducted to  the  lower  bluff  on  the  American  side,  and  distributed,  by 
open  canals,  to  various  plants  located  along  this  bluff.. 

The  second  plant  constructed  was  chat  of  The  Niagara  Falls 
Power  Company,  in  which  power  is  developed  by  the  vertical  shafts 
connecting  with  a  tail-water  tunnel  which  discharges  into  the  river 
just  below  the  new  suspension  bridge. 


578  The  Relation  of  Dam  and  Power  Station. 

On  the  Canadian  side  are  shown  three  plants. 

The  Ontario  Power  Company  secures  its  water  supply  from  the 
upper  portion  of  the  rapids,  conducting  it  through  steel  conduits 
to  a  point  above  the  power  house  and  thence  by  penstocks  to  the 
wheel,  located  in  the  gorge  below  the  falls. 

In  the  plants  of  The  Toronto  and  Niagara  Power  Company  and 
The  Canadian-Niagara  Power  Company,  the  water  is  taken  from 
above  the  Falls  and  discharges  through  penstocks  to  wheels  located 
at  the  base  of  a  shaft  and  thence  into  tunnels,  discharging  into  the 
river  at  a  point  below  the  Falls. 

Fig.  355  illustrates  the  plant  of  The  Niagara  Falls  Hydraulic  and 
Manufacturing  Company,  which  is  supplied  by  water  from  the 
hydraulic  canal  above  mentioned.  The  water  is  conducted  from  the 
forebay  by  a  vertical  penstock  to  which  is  attached  several  wheels 
which  deliver  the  water  into  a  tail-race  tunnel  and  thence  into  the 
gorge  below. 

The  plant  arrangements  above  described  are  typical  of  many  now 
in  use  both  in  this  country  and  in  Europe.  It  is  at  once  obvious  that 
in  considering  this  subject  each  particular  location  is  a  problem  by 
itself  which  must  be  considered  in  all  its  bearings ;  but  an  under- 
standing of  the  designs  and  arrangements  already  in  use  forms  a 
satisfactory  basis  fromi  which  a  judicious  selection  can  be  made 
with  suitable  modifications  to  take  care  of  all  the  conditions  of 
topography  and  other  controlling  conditions. 


CHAPTER  XXIV. 

PRINCIPLES   OF    CONSTRUCTION    OF    DAMS. 

291.  Object  of  Construction. — A  dam  is  a  structure  constructed 
with  the  object  of  holding  back  or  obstructing  the  flow  and  elevat- 
ing the  surface  of  water.     Such  structures  may  be  built  for  the  fol- 
lowing purposes : 

First :  To  concentrate  the  fall  of  a  stream  so  as  to  admit  of  the 
economical  development  of  power. 

Second :  To  deepen  the  water  of  a  stream  so  as  to  facilitate  nav- 
igation and  to  so  concentrate  the  fall  that  vessels  may  be  safely 
raised  from  a  lower  to  an  upper  level  by  means  of  locks. 

Third :  To  impound  or  store  water  so  that  it  may  be  utilized  as 
desired  for  water  supply,  water  power,  navigation,  irrigation,  or 
other  uses. 

Fourth :  In  the  form  of  mine  dams  or  bulk  heads  to  hold  back 
the  flow  of  water  which  would  otherwise  flood  mines  or  shafts  or 
cause  excessive  expense  for  its  removal. 

Fifth:  As  coffer-dams  for  the  purpose  of  making  accessible, 
usually  for  construction  purposes,  submerged  areas  otherwise  inac- 
cessible. 

292.  Dams  for  Water  Power  Purposes. — The  primary  object  of 
a  dam  constructed  for  water  power  purposes  is  to  concentrate  the 
fall  of  the  stream  so  that  it  can  be  developed  to  advantage  at  one 
point  and  so  that  the  water  thus  raised  can  more  readily  be  delivered 
to  the  motors  through  raceways  and  penstocks  of  reasonable  length. 
This  object  is  sometimes  accomplished  in  rivers  with  steep  slopes 
or  high  velocities  by  the  construction  of  wing  dams  which  occupy 
only  a  portion  of  the  cross-section  of  the  stream,  but  cause  a  head- 
ing up  of  the  water  and  direct  a  certain  portion  of  the  flow  into 
the   channel   or   raceway   through  which   it   flows   to  the   wheels. 
Usually  in  streams  of  moderate  slope  the  dam  must  extend  entirely 
across  the  stream  in  order  to  concentrate  sufficient  head  to  be  of 
practical  utility. 


580  Principles  of  Construction  of  Dams. 

Wing  dams  can  be  used  at  the  head  of  high  falls  where  only  a 
portion  of  the  volume  of  flow  can  be  utilized,  as  at  Niagara  Falls, 
or  in  rapid  rivers  wrhere  a  portion  of  the  flow  is  to  be  directed  into 
a  narrow  channel  for  utilizing  low  heads  by  means  of  undershot  or 
float  wheels  as  is  frequently  done  for  irrigation  purposes.  Where 
the  full  benefit  of  both  head  and  volume  is  to  be  utilized  the  dam 
must  extend  from  bank  to  bank  and  be  constructed  of  as  great  a 
height  as  possible. 

293.  Height  of  Dam. — To  utilize  a  river  to  the  maximum  extent 
the  highest  dam  practicable  must  be  constructed. 

The  height  of  a  dam  may  be  limited  by  the  following  factors : 

First :  The  overflow  of  valuable  lands. 

Second:  The  interference  with  water  power  rights  above  the 
point  of  development. 

Third :  The  interference  with  other  vested  or  public  rights. 

Fourth :  The  cost  of  the  structure. 

The  value  of  the  power  that  can  be  developed  by  means  of  a  pro- 
posed dam  will  limit  the  amount  that  can  be  expended  in  the  pur- 
chase or  condemnation  of  property  affected  by  backwater  from  the 
dam  and  the  cost  of  its  construction.  These  are  among  the  ele- 
ments of  the  cost  of  the  project  and  must  be  considered  together 
with  other  financial  elements  before  a  water  power  project  can  be 
considered  practicable. 

In  considering  backwater  and  its  effect  on  riparian  rights  both 
high  and  moderate  conditions  of  flow  must  be  considered.  The 
former  condition  gives  rise  to  temporary  interference,  often  of  little 
importance  when  affecting  purely  farming  property,  and  the  real 
or  fancied  damages  from  which  can  commonly  be  liquidated  by  re- 
leases at  small  expense.  The  latter  condition  will  permanently 
inundate  certain  low  lands  which  must  be  secured  by  purchase  or 
condemnation.  In  many  states  where  the  laws  of  eminent  domain 
do  not  apply  to  the  condemnation  of  property  for  such  purposes  it 
is  necessary  to  secure  such  property  by  private  purchases  before 
the  work  is  undertaken,  and  usually  before  the  project  becomes 
known  publicly,  for  in  such  cases  the  owner  of  a  single  piece  of  land 
may  delay  the  project  by  a  demand  for  exorbitant  remuneration, 
from  which  demand  there  is  in  such  cases  no  escape-  In  every  case 
it  is  desirable  that  riparian  and  property  rights  be  fully  covered 
before  the  construction  of  the  project  actually  begins. 


The  Foundation  of  Dams.  581 

294.  Available  Head. — Beside  the  question  of  backwater  the  ques- 
tion of  head  at  the  dam  is  important  both  in  relation  to  the  question 
of  interference  and  in  relation  to  the  question  of  power.    In  relation 
to  interference  it  is  an  easy  matter  with  a  known  length  and  height 
of  dam  to  determine  by  calculation  from  a  properly  selected  weir 
formula  the  height  of  water  above  the  dam  under  any  condition  of 
flow.    To  determine  the  head  available  under  all  conditions  of  flow 
the  weir  curve  must  be  studied  in  connection  with  the  rating  curve 
as  discussed  in  Chapter  V. 

Two  conditions  of  flow  often  require  consideration  in  this  con- 
nection : 

First :  Where  a  considerable  portion  of  the  flow  is  being  utilized 
by  the  wheels  and  therefore  does  not  affect  the  head  of  the  dam. 

Second:  Where  the  water  is  not  being  used  by  the  wheels  and 
consequently  affects  the  head  of  the  dam. 

Both  of  these  conditions  should  be  studied  and  determined  in  rela- 
tion to  their  influence  on  both  backwater  conditions  and  power. 

295.  The  Principles  of  Construction  of  Dams. — The  general  prin- 
ciples for  the  construction  of  all  dams  are  similar,  and  are  as  fol- 
lows : 

First :  They  must  have  suitable  foundations  to  sustain  the  pres- 
sure transmitted  through  them,  which  must  be  either  impervious  or 
rendered  practically  so. 

Second  :  They  must  be  stable  against  overturning. 

Third :  They  must  be  safe  against  sliding. 

Fourth :  They  must  have  a  sufficient  strength  to  withstand  the 
strains  and  shocks  to  which  they  are  subjected. 

Fifth :  They  must  be  practically  water-tight. 

Sixth :  They  must  have  essentially  water-tight  connections  with 
their  beds  and  banks,  and,  if  bed  or  banks  are  pervious,  with  some 
impervious  stratum  below  the  bed  and  within  the  banks  of  the 
stream. 

Seventh :  They  must  be  so  constructed  as  to  prevent  injurious 
scouring  of  the  bed  and  banks  below  them. 

The  application  of  the  above  principles  depends  on  the  material 
.from  which  the  dam  is  to  be  built  and  on  local  conditions- 

296.  The  Foundation  of  Dams. — The  materials  used  for  the  con- 
struction of  dams  may  be  masonry,  which  includes  stone-work  and 
concrete-work,   reinforced  concrete,  timber,   steel,  loose  rock,  and 
earth.      Each    may    be    used    independently    or    in    combination. 
Masonry  and  concrete  dams  must  be  built  upon  foundations  which 


582  Principles  of  Construction  of  Dams. 

are  practically  free  from  possible  settlement.  Small  masonry  struc- 
tures may  sometimes  be  safely  constructed  on  piles  or  grillage 
foundation  based  on  softer  materials ;  but  the  larger  and  more  im- 
portant structures,  if  constructed  of  masonry,  can  be  safely  built 
only  upon  solid  rock.  Reinforced  concrete  is  now  being  extensively 
used  for  small  structures  and  is  not  as  seriously  affected  by  slight 
settlement  as  in  the  case  of  dams  of  solid  masonry.  There  is,  how- 
ever, little  flexibility  in  structures  of  this  kind,  and  the  foundation 


Fig.  356.— Timber  Crib  Dam  at  Janes ville,  Wis. 

must  be  selected  in  accordance  with  this  fact.  Timber  and  steel 
possess  a  flexibility  not  possible  in  concrete  construction  and  are 
much  better  adapted  to  locations  where  the  foundation  may  be  sub- 
ject to  settlement. 

In  construction  on  rock  foundation  it  is  usually  desirable  to  exca- 
vate trenches  therein  in  order  to  give  a  bond  between  the  structure 
of  the  dam  and  its  foundation.  It  is  also  essential  with  rock  foun- 
dations to  determine  whether  cracks  or  fissures  in  the  foundation 
extend  below  the  structure,  and  if  such  are  found,  they  must  be 
completely  cut  off. 

On  earth,  sand  or  gravel  foundations,  when  such  must  be  used, 
the  flow  which  would  take  place  through  these  materials  and  under 
the  structure  of  the  dam  must  be  completely  cut  off  by  the  use  of 
steel  or  timber  sheet  piling,  which,  if  possible,  should  be  driven 
from  the  structure  to  the  rock  or  to  some  other  impervious  stratum. 
If  no  impervious  stratum  is  accessible,  the  sheet  piling  must  be 


Strength  of  Dams.  583 

driven  to  such  a  distance  below  the  base  of  the  dam  that  the  friction 
of  the  flow  of  water  under  it  will  reduce  or  destroy  the  head  and 
consequently  reduce  the  flow  of  water  to  an  inappreciable  quantity. 
297.  Strength  of  Dams. — A  dam  to  be  built  in  a  flowing  stream 
should  be  designed  with  a  full  appreciation  of  all  the  stresses  to 
which  it  may  be  subjected.  Of  these,  stresses  that  are  due  to  static 
pressure  can  be  readily  estimated  from  the  known  conditions.  The 
strains  due  to  dynamic  forces  are  not  so  fully  understood  or  easily 


Fig.  357.— Janesville  Dam  with  Moderate  Water. 

calculated.  Where  the  structure  is  constructed  to  retain  a  definite 
head  of  water  without  overflow,  as  in  the  case  of  reservoir  embank- 
ments, the  problem  becomes  one  largely  of  statics  and  the  only 
other  stresses  to  be  considered  are  those  due  to  ice  action  and  the 
action  of  waves  on  the  structure.  When  a  dam  is  constructed  in  a 
running  stream  and  is  subject  to  the  passage  of  extensive  floods  of 
water  over  it,  frequently  accompanied  by  large  masses  of  floating 
ice,  logs  or  other  material  which  in  many  cases  may  strike  the 
crest  of  the  dam,  and  bring  unknown  and  violent  strains,  the  prob- 
lem becomes  largely  one  of  experience  and  judgment. 

298.  Flood  Flows. — The  passage  of  great  volumes  of  water  over 
a  dam  involves  the  expenditure  of  the  power  so  generated  upon  or 
immediately  adjoining  the  structure,  and  unless  preparations  are 
made  for  properly  taking  care  of  this  immense  expenditure  of 
power,  the  power  may  be  exerted  in  the  destruction  of  the  structure 
itself. 


584 


Principles  of  Construction  of  Dams. 


Figs.  356  to  358  show  three  views  of  the  timber  <!rib  dam  at 
Janesville,  Wisconsin,  under  various  conditions  of  flow.  In  Fig. 
356  the  flow  of  the  river  is  comparatively  small  and  all  of  the  water 
is  being  used  in  the  power  plant,  none  passing  over  the  dam.  In 
Fig.  357  the  river  is  at  a  moderate  stage  and  the  greater  part  of  the 
flow  is  passing  over  the  crest  of  the  dam.  In  Fig.  358  some  four 
or  five  feet  of  water  is  passing  over  the  dam  and  the  power  that  is 
•developed  thereby  is  causing  the  standing  wave  and  the  rough 


Fig.  358. — Janesville  Dam  under  High  Water. 

water  shown  in  the  picture  below  the  dam.  At  this  point  the  power 
developed  by  the  fall  is  being  expended  in  waves  and  eddies,  which, 
unless  properly  controlled,  will  attack  and  injure  or  destroy  the 
structure.  On  rock  bottom  the  rock  itself  will  sustain  the  impact  of 
flow  over  small  dams.  But  where  the  rock  is  soft,  or  the  bottom  is 
composed  of  material  that  can  be  readily  disintegrated,  it  becomes 
necessary  to  extend  the  structure  of  the  dam  itself  in  the  form  of 
an  apron  to  cover  and  protect  the  bottom. 

Fig.  359  shows  the  preliminary  design  of  a  dam  for  the  Southern 
Wisconsin  Power  Company,  now  under  construction  at  Kilbourn, 
Wisconsin.  This  dam  will  be  about  17  feet  in  height  above  low 
water  and  will  be  subject  at  times  to  the  passage  of  floods  to  a 
depth  of  16  feet  above  its  crest.  For  section  of  dam  as  constructed 
see  Fig.  373.  The  two  ends  of  the  dam  will  rest  upon  a  rock 
foundation.  Cribs  are  also  carried  to  the  rock  at  the  face  of  the 
dam  and  at  the  edge  of  the  apron.  The  center  of  the  dam  is  sus- 


Flood  Flows. 


585 


586  Principles  of  Construction  of  Dams. 

tained  by  piles  reaching  to  rock  but  surrounded  by  sand  which  is 
retained  by  the  cribs. 

The  dam  proper  is  built  of  cells  6  feet  square,  the  walls  of  each 
cell  being  built  of  solid  timber,  and  each  cell  carefully  filled  with 
stone  and  sand.  At  the  face  of  the  dam  and  at  the  toe  of  the  apron 
triple  sheeting  has  been  placed  and  securely  fastened  to  the  dam 
and  cribs  from  the  rock  up,  thus  effectively  preventing  the  passage 
of  water  below  or  through  the  dam. 

During  high  floods  the  amount  of  power  which  must  be  wasted  in 
the  passage  of  water  over  the  dam  will  exceed  100,000  horse  power. 
In  order  to  prevent  the  expenditure  of  this  power  in  the  destruction 
of  the  dam,  the  dam  is  extended  in  an  apron  of  about  100  feet  in 
width.,  the  total  width  of  the  structure  including  the  dam  and  the 
apron,  being  about  150  feet. 

To  further  protect  the  structure,  rip-rap  is  deposited  both  above 
and  below  the  structure  itself.  The  surface  of  the  dam  exposed  at 
times  of  low  water  is  constructed  of  re-inforced  concrete,  attached 
directly  to  the  timber  work  of  steel  reinforcement.  By  this  design 
a  structure  is  obtained  having  all  the  advantages  of  the  flexibility  of 
timber,  with  the  lasting  qualities  of  masonry,  for  the  concrete  only 
will  be  exposed  at  times  of  low  water,  all  timber  work  being  sub- 
merged under  every  ordinary  condition. 

299.  Impervious    Construction — Masonry    dams    are    commonly 
made  impervious  by  the  structure  of  the  masonry  itself. 

In  timber  crib  dams  ordinarily  no  attempt  is  made  to  make  the 
structure  itself  water-tight,  but  the  top  and  upstream  side  are  usu- 
ally covered  with  wafer-tight  sheeting  to  prevent  the  wrater  pass- 
ing into  and  through  the  cribs.  Such  water  as  reaches  the  timber 
cribs  usually  passes  away  readily  through  the  open  structure  on  the 
down,  stream  side  of  the  dam. 

In  the  construction  of  rock-filled  dams  the  same  condition  ordi- 
narily obtains.  The  dam  is  fairly  porous  with  the  exception  of  its 
upper  face  which  is  made  practically  water-tight  by  the  use  of  con- 
crete, puddle,  or  some  impervious  paving. 

In  earthen  dams  the  finer  and  more  water-tight  materials  are 
used  on  the  inner  slopes  of  the  embankment,  and,  in  addition 
thereto,  it  is  customary  in  large  and  important  works  to  use  a  core 
of  concrete  or  puddle  to  effectively  prevent  the  passage  of  water 
through  the  structure. 

300.  The  Stability  of  Masonry  Dams. — The  external  forces  act- 
ing on  a  masonry  dam  are  the  water  pressure,  the  weight  of  the 


Stability  of  Masonry  Dams.  587 

masonry,  the  reaction  of  the  foundation,  ice  and  wave  pressure  near 
the  top,  wind  pressure,  and  back  pressure  of  the  water  on  the  down 
stream  side.  The  action  of  these  forces  may  cause  a  dam  to  fail  by : 

(1)  Sliding  on  the  base  or  on  any  horizontal  plane  above  the 
base. 

(2)  Overturning. 

(3)  Crushing  the  masonry  or  foundation. 

If  the  dam  be  built  of  rubble  masonry  there  will  be  no  danger  of 
failure  by  sliding  on  a  horizontal  joint  above  the  foundation  and 
experience  has  shown  that  where  a  good  quality  of  mortar  is  used 
it  can  be  depended  upon  to  prevent  sliding  in  concrete  and  stone 
dams  having  horizontal  bed  joints.  The  joint  between  the  dam  and 
its  foundation  is  a  more  critical  point.  In  rock  foundation  steps  or 
trenches  should  be  cut  so  as  to  afford  good  anchorage  for  the  dam. 
In  the  case  of  clay,  timber  or  similar  foundations  the  dam  will  have 
to  be  made  massive  enough  so  that  the  tangent  of  the  angle  be- 
tween the  resultant  pressure  on  the  base  and  a  vertical  line  is  less 
than  the  co-efficient  of  friction  between  the  materials  of  the  dam 
and  the  foundation. 

It  is  customary  in  the  design  of  masonry  dams  to  proportion  the 
section  so  that  the  lines  of  resultant  pressure  at  all  horizontal 
joints,  for  both  the  conditions  of  reservoir  full  and  reservoir 
empty,  shall  pass  through  the  middle  third  points  of  the  joints. 
If  this  condition  is  fulfilled,  the  factor  of  safety  against  overturn- 
ing at  every  joint  will  be  2,  and  there  will  also  be  no  danger  from 
tensile  stresses  developing  in  the  faces  of  the  dam. 

Investigation  has  shown  that  there  is  no  danger  of  crushing  the 
masonry  except  in  very  high  dams,  with  the  consideration  of  which 
we  are  not  here  concerned- 

301.  Calculation  for  Stability. — The  general  conclusion  may  there' 
fore  be  stated,  that,  in  the  case  of  ordinary  masonry  and  con- 
crete dams,  not  over  100  feet  in  height,  to  be  built  on  rock  foun- 
dations, the  design  can  be  based  upon  the  condition  that  the  lines 
of  pressure  must  lie  within  the  middle  third  of  the  profile 
This  rule  must  be  modified  at  the  top  of  the  dam  to  resist  the 
stresses  due  to  waves,  ice,  etc.  The  force  exerted  by  ice  is  an  in- 
determinate quantity  and  the  tops  of  dams  must  therefore  be  pro- 
portioned in  accordance  with  empirical  rules.  Dams  are  built  with 
top  widths  varying  from  2  to  22  feet,  the  broader  ones  usually 


588 


Principles  of  Construction  of  Dams. 


carrying  a   roadway.     Coventry  suggests  the   following  empirical 
rules  for  width  of  top  and  height  of  top  above  water  level : 

(1)  b    =  4.0  +  0.07H 

(2)  y0  =  1.8  + 0.05  H 

Where  b  is  the  width  of  top,  y0  the  height  above  water  level  and 
H  the  greatest  depth  of  water.  Both  faces  of  the  dam  will  be  ver- 
tical until  the  depth  y,  is  reached,  where  the  resultant  force  passes 
through  the  middle  third  point.  Below  this  depth  the  general  rule 
will  apply.  In  computing  the  water  pressure  against  the  dam,  it 


Fig.  360. 


is  best  to  consider  the  water  surface  level  with  the  top  of  the  dam 
in  order  to  allow  for  possible  rises  due  to  floods,  etc.  Having  de- 
termined the  top  width,  b,  and  assuming  a  section  of  the  dam  one 
foot  long,  the  height,  y,  of  the  rectangular  portion  can  be  deduced 
from  the  formula 


in  which  s  is  the  specific  gravity  of  the  material  of  the  dam. 

The  down-stream  face  of  the  dam  must  now  be  sloped  so  as  to 
keep  the  resultant  pressure,  with  the  reservoir  full,  at  the  limit  of 
the  middle  third  of  the  length  of  any  joint  Dividing  the  remainder 
of  the  height  of  the  dam  into  lengths  convenient  for  computation, 
the  length  of  any  joint,  (see  Fig.  360)  as  "Gil  may  be  found  by  the 
formula 


Calculation  for  Stability.  589 


(4)  GIT  =  l/B  +  C8  —  C 

in  which 


B  _  6  m  (Area  ABFE)     +     BH;      +  ^ 

¥H~  s^lT 

where  m  =  distance  from  F  of  the  line  of  action  of  the  weight  of 
masonry  above  EF  and 


c  _  i  ["4  (Area  ABFE)  +  ^ 
The  value  of  n  is  given  by  the  equation 


,-x  Mom.  of  ABFE  +  Mom.  of  EFHG 

(0)  n — —         

(Area  ABHG) 

moments  being  taken  about  the  point  H. 

Equation  (4)  can  be  used  as  long  as  n  is  greater  than  one-third 
the  length  of  the  joint.  When  this  condition  can  no  longer  be  sat- 
isfied with  a  vertical  face;  it  will  be  necessary  to  batter  the  upstream 
face  also,  so  that  the  lines  of  pressure  with  reservoir  full  and  empty 
both  lie  at  the  limits  of  the  middle  third  of  the  length  of  any  joint. 

The  length  of  the  joints,  as  IJ,  may  now  be  found  by  the  formula 

(6)      IJ  =  V- 

sHK 

and  the  value  of  KJ,  is 

tPr  _  2  (Area  ABHG)    ( IJ  —  3m)  -  (~HK    X  ~GH8) 

{I  )  J\.J     —    — ====^ ^^^z 

6  (Area  ABHG)  +  HK    (2GH    +  IJ) 

In  high  dams  two  more  stages,  governed  by  the  compressive 
strength  of  the  masonry,  would  have  to  be  considered,  but,  within 
the  limit  of  height  set  above,  the  formulas  given  are  sufficient. 

The  position  of  the  line  of  pressure  may  be  readily  determined 
also  by  graphical  methods. 

In  the  case  of  overfall  dams,  which  are  necessarily  subjected  to 
dynamic  forces,  which  are  more  or  less  indeterminate,  the  design 
cannot  be  so  closely  figured- 

302.  Further  Considerations. — The  preceding  analysis  does  not 
take  into  account  the  possibility  of  an  upward  pressure  from  below 
the  dam,  due  to  the  pervious  character  of  the  foundation,  or  to 
cracks  and  fissures,  by  means  of  which  the  pressure  of  the  head 
water  may  be  transmitted  to  the  base  of  the  dam.  This  factor  is 
commonly  ignored  in  dam  construction,  but  should  be  considered, 
36 


590  Principles  of  Construction  of  Dams. 


Elevation 


Fig.  361. — Cross-section  of  Dam  of  Holyoke  Water  Power  Co. 


Fig.  362. — Masonry  Dam  of  Holyoke  Water  Power  Co. 


Further  Considerations. 


591 


and,  when  occasion  requires,  the  foundation  should  be  so  prepared 
as  to  obviate  or  reduce  it  to  a  minimum.  This  may  usually  be  done 
by  the  careful  preparation  of  the  foundation  to  prevent  inflow,  or  by 
the  construction  of  drains  from  the  interior  of  the  foundation  to  the 
lower  face. 

The  construction  of  a  dam  with  a  vertical  overfall,  unless  pro- 
vision is  made  for  the  admission  of  air,  will  result  in  the  formation 
of  a  partial  vacuum  below  the  sheet,  and  a  certain  extra  strain  on 


Fig.  363. — Holyoke  Dam  During  Flood. 

the  structure  due  to  the  same.  The  vertical  overfall  is  also  fre- 
quently objectionable,  on  account  of  the  action  of  the  falling  water 
on  the  bed  of  the  stream  immediately  adjacent  to  the  dam,  and 
on  the  foundation  of  the  dam  itself.  It  is  frequently  desirable  to  give 
the  lower  face  of  the  dam  a  curved  outline,  in  order  to  guide  the 
water  smoothly  over  the  dam,  and  deliver  it  approximately  tangen- 
tial to  the  stream  bed.  The  convex  surface  of  the  dam  should  be 
of  such  form  that  the  water  will,  through  gravity,  adhere  to  it. 
An  example  of  a  dam  with  a  curved  face  is  shown  by  Fig.  361 
which  is  a  section  of  the  dam  of  the  Holyoke  Water  Power  Com- 
pany. Two  views  of  the  dam,  one  during  low  water  (Fig.  362) 
and  one  with  about  ten  feet  of  water  flowing  over  the  crest  (Fig. 


592 


Principles  of  Construction  of  Dams. 


363)  are  also  shown.  A  section  of  the  McCall's  Ferry  dam,  built  of 
Cyclopean  Concrete  (height  53  feet)  is  shown  in  Fig.  364  and  a  sec- 
tion of  a  small  Concrete  dam  at  Danville,  111.,  is  shown  in  Fig.  365. 
The  curve  for  dams  of  this  character  should  be  kept  at  or  above  the 


Fig.  364.  —  Section  of  McCall  Ferry  Dam   (Eng.  Rec.). 

parabolic  path  that  the  water  would  take  in  a  free  fall  with  the  in- 
itial horizontal  velocity  corresponding  to  the  depth  of  water  on  the 
dam. 

From  equation  50,  page  64,  the  flow  over  one  foot  of  crest  will 
equal, 

q  =  vh  =  ra(f)T/2g  hi,        tience, 
v  =  m 


The  abscissa  of  the  parabola  is  x  =  vt,  .in  which  t=  time  in 
seconds. 


•Flash  Boards 


Timbers,  6xK" 


Fig.  365-Concrete  Dam,  Danville,  111. 


Timber  Crib  Dam  at  Butte,  Montana. 


593 


594 


Principles  of  Construction  of  Dams. 


The  ordinate  is,  y  =  %  gt2,  hence. 

y  =  -^  x  is  the  equation  of  the  parabola.  * 

When  a  curved  face  is  impracticable  or  undesirable  and  the  bed 
of  the  stream,  below  the  dam,  is  not  of  suitable  material  to  resist 
the  impact  of  the  falling  water,  some  form  of  apron  must  be  pro- 
vided. Sometimes  the  dam  is  divided  into  steps  over  which  the 
water  falls  in  numerous  cascades.  Such  a  dam  is  shown  in  Fig. 
366.  This  is  the  timber  crib  dam  constructed  for  the  Montana 


pi/ma 


.  Fig.  367.— Timber  Dam  at  Sewall  Falls.     (Eng.  News,  vol.  XXXI.) 

Power  Company,  near  Butte,  Montana.  In  this  case  the  cells  are 
composed  of  timber,  laid  alternately  in  each  direction,  with  a  con- 
siderable space  left  between  them,  instead  of  being  built  solid  as 
in  the  Kilbourn  dam.  These  cells  were  filled  with  broken  stone, 
and  the  upstream  side  of  the  dam  was  planked  with  sheeting  in 
order  to  make  the  structure  water-tight.  When  the  water  was 
admitted  behind  the  dam  a  portion  of  the  structure  was  forced 
out  of  alignment  by  the  crushing  of  the  timbers,  at  the  points  of 
contact.  The  amount  of  this  displacement  and  the  cause  of  the 
same  is  quite  clearly  shown  in  the  cut. 

Fig.  367  is  a  section  of  the  Sewall  Falls  dam,  showing  a  similar 
method  of  resisting  the  impact  of  the  overflow. 

304.  Types  and  Details  of  Dams. — The  types  of  dams  are  so  nu- 
merous, and  the  details  of  construction  vary  so  greatly  with  every 
locality,  that  an  entire  volume  would  be  necessary  to  adequately 
cover  this  subject.  As  the  subject  is«already  well  covered  in  many 
special  treatises  and  articles,  no  attempt  will  be  made  to  discuss 
this  subject  in  the  present  edition.  Numerous  references  are  given 
to  books  and  articles  in  which  special  forms  of  construction  are 
discussed  and  described. 

*  Turneaure  &  Eussell's  "Public  Water  Supplies,"  Section  446. 


Literature.  595 


LITERATURE. 

PRINCIPLES    OF    CONSTRUCTION    OF   DAMS. 

1.  Turneaure  and  Russell.     Public  Water  Supplies.     Chaps.  16  to  18.     John 

Wiley  and  Sons,  1901. 

2.  Church,  I.  P.     Mechanics  of  Engineering.     John  Wiley  and  Sons,  1904. 

3.  Wegmann,  Edward.     The  Design  and  Construction  of  Dams.     John  Wiley 

and  Sons,  1899. 

4.  Leffell,  James.     Construction  of  Mill  Dams.     James  Leffell  and  Company, 

Springfield,  Ohio,  1881. 

5*.  Follet,  W.  W.     Earthen  vs.   Masonry   Dams.     Eng.  News,   Jan.   2,   1892, 
et  seq.     Eng.  Rec.  May  14,  1892,  et  seq. 

6.  Hall,  P.  F.     Investigation  of  the  Distribution  of  Pressure  on  the  Base  of 

Dams.     Trans.  Assn.  C.  E.  of  Cornell,  1900. 

7.  Knight,  Frank  B.     Building  an  Impounding  Dam  for  Storage  Reservoir. 

Mines  and  Mining,  May,  1900, 

8.  Schuyler,  Jas.  Dix.     Reservoirs  for  Irrigation,  Water  Power  and  Domes- 

tic Water  Supply.     New  York.    Wiley  and  Sons,  1901. 

9.  Gregory,  John  H.     Stability  of  Small  Dams.     Eng.  Rec.  Sept.  21,  1901. 

10.  Fielding,   John   S.     Essential   Elements   in   the   Design   of   Dams.     Can. 

Ehgr.     Jan.  1905. 

11.  Wilson,  J.  S.,  and  Gore,  W.     Stresses  in  Dams.     Engng.    Aug.  4,  1905. 

STABILITY    OF    MASONRY    DAMS. 

1.  Coventry,  W.   B.     Design  and   Stability  of  Masonry   Dams.     Proc.   Inst. 

C.  E.  vol.  85,  p.  281.     1886.    . 

2.  Morley,   Isaac.     On  the  Determination  of  the  Profile  of  High  Masonry 

Dams.     Eng.  News,  Aug.  11,  1888. 

3.  Vischer   and   Waganer.     The    Strains   in    Curved   Masonry    Dams.     Eng. 

News,  Mch.  15,  1890;   Sept.  27,  1890. 

4.  Van  Buren,  John  D.     Notes  on  High  Masonry  Dams.     Trans.  Am.  Soc. 

C.  E.  vol.  34,  p.  493.     Dec.  1895. 

5.  Pelletiau,  M.     Profiles  for  Masonry  Dams.     Ann.  des  Fonts  et  Chaussees. 

Feb.  1,  1897. 

6.  Levy,  Maurice.     Trapezoidal  Formula.     Comptes  Rendus.     May  2,  1898. 

7.  Levy,  Maurice.     The  Elastic  Equilibrium  in  a  Masonry  Dam  of  Triangu- 

lar  Section.     Comptes   Rendus.     July   4,   1898. 

8.  Specifications  for  a  Large  Concrete  Dam.     Eng.  Rec.     Oct.  29,  1898. 

9.  Bainet,  M.     The  Computation  of  Masonry  Dams  for  Reservoirs.     Ann  des 

Fonts  et  Chaussees.     2  Trimestre  1898. 

10.  Baibet,  M.  L.     The  Conditions  of  Resistance  of  Masonry  Dams  for  Reser- 

voirs.    Ann  des  Fonts  et  Chaussees.     1  Trimestre  1899. 

11.  Dillman,  Geo.  L.     A  Proposed  New  Type  of  Masonry  Dam.     Trans.  Am. 

Soc.  C.  E.  vol.  49,  p.  94.     1902. 


Principles  of  Construction  of  Dams. 

12.  Wisner,   Geo.   Y.     The  Correct   Design   and   Stability   of   High   Masonry 

Dams.     Eng.  News.     Oct.  1,  1903. 

13.  Stability  of  Masonry  Dams.     Engng.     Mch.  31,  1905. 

14.  Review  of  Paper  of  Atcherly  &  Pearson  on  Stability  of  Masonry  Dams. 

Engr.,   Lond.    Mch.   31,   1905. 

15.  Unwin,  W.  C.     Note  on  the  Theory  of  Unsymmetrical   Masonry   Dams. 

Engng.     Apr.  21,  1905. 

16.  Unwin,  W.  C.     Further  Notes  on  the  Theory  of  Unsymmetrical  Masonry 

Dams.     Engng.     May  12,  1905. 

17.  Unwin,  W.  C.     On  the  Distribution  of  Shearing  Stresses  in  Masonry  Dams. 

Engng.     June  30,  1905. 

18.  Pearson,    Karl.     On    the    Stability    of    Masonry    Dams.     Engng.    vol.    80, 

July  14,  1905. 

19.  Wisner,  Geo.  Y.,  and  Wheeler,   Edgar  T.     Investigation  of  Stresses   in 

High  Masonry  Dams  of  Short  Spans.     Eng.  News.  Aug.  10,  1905. 

20.  Pearson,  Karl.     On  the  Stability  of  Masonry  Dams.     Engineering,  vol.  80, 

p.  171.     Aug.  11,  1905. 

21.  The  Determination  of  Pressures  on  Masonry  Dams.     Oest.  Wochenschr. 

f  d  Oeff.  Baudienst.     Aug.  19,  1905. 

22.  Bleich,  S.  D.     Internal  Stresses  in   Masonry  Dams.     Sch.  of  Mines  Qr. 

Nov  1905. 

23.  Ende,  Maxam.     Notes  on  Stresses  in  Masonry  Dams.     Engineering.     Dec. 

1905. 

EARTHEN   DAMS. 

1.  Fitzgerald,  J.   L.     Leakage  Through  an  Earthen   Dam  at  Lebanon,  Pa. 

Eng.  Rec.     May,  1893,  pp.  474-5. 

2.  LeConte,  L.  J.     High  Earthen  Dam  for  Storage  Reservoirs.     Proc.  Am. 

W.  Wks.  Assn.,  1893,  and  Eng.  Rec.  Sept.  16,  1893. 

3.  Fitzgerald,  D.,  and  Fteley,  A.     Construction  of  Reservoir  Embankments. 

Eng.  News.     Oct.  26,  1893.     pp.  330-1. 

4.  Earth  Dam  of  the  Honey  Lake  Valley,  California.     Eng.  News,  Mch.  15, 

1894. 

5.  Earth  Dam  at  New  Britain,  Conn.     Eng.  Rec.     June  23,  1894. 

6.  Difficulties  with  Earth  Dams  in  Great  Britain.     Eng.  Rec.     Set.  3,  1898. 

7.  Strange,   W.    L.     The    Construction    of    High    Earth    Dams.     Eng.    Rec. 

Apr.  15,  1899. 

8.  The  Limiting  Heights  of  Earth  Dams.     Eng.  Rec.     Dec.  7,  1901. 

9.  A  Remarkable  Core-wall  for  an  Earth  Dam.     Eng.  Rec.     Dec.  21,  1901. 

10.  Concerning  the    Design    of   Earth    Dams   and   Reservoir    Embankments. 

Eng.  News,  Feb.  20,  1902. 

11.  The  Tabeaud  High  Earth  Dam,  near  Jackson,  Cal.     Eng.  News.     July  10, 

1902. 

12.  Bassell,    Burr.     The   San    Leandro    Earth    Dam    of    the   Oakland    Water 

Works.     Eng.  News,  Sept.  11,  1902. 

13.  The  New  Earth  Dam  for  Water  Works  of  Santa  Fe,  N.  M.     Eng.  News, 

Apr.  13,  1903,  p.  346. 


Literature.  597 

14.  An  Earth  Dam  with  Loam  Core  at  Clinton,  Mass.     Eng.  Rec.     Aug.  20, 

1904. 

15.  Brown,  R.  H.     Grouted  Rubble  Core  Walls  for  the  Weirs  of  the  Delta 

Barrage,  Egypt.     Eng.  News,  Feb.  9,  1905. 

16.  Walter,  Raymond  F.     Belle  Fourche  Dam,  Belle  Fourche  Project,  S.  D. 

Eng.  Rec.     Mch.  3,  1906.     Vol.  53,  p.  307. 

17.  Herschel,  Clemens.     Earth  Dams  with  Concrete  Core  Walls.     Eng.  News, 

Sept  7  1905. 

18.  Leonard,  J.  A.     A  Proposed  Earth  Dam  with  a  Steel  Core  and  a  Rein- 

forced Concrete  Spillway  at  Ellsworth,  Me.     Eng.  News,  Sept.  7, 
1905. 

19.  Schuyler,  J.   D.     Recent  practice   in  Hydraulic  Fill  Dam  Construction. 

Proc.  Am.  C.  E.  Oct.  1906. 

BOCK    FILL    DAMS. 

1.  The  Otay  Dam.     Eng.  Rec.     Sept.  28,  1895,  p.  310. 

2.  The  Nevada  County  Electric  Power  Company's  Dam.     Min.  &   Sci.   Pr. 

Feb.  8.  1896. 

3.  A  Rock-fill  Dam  with  a  Steel  Heartwall  at  Otay,  Cal.     Eng.  News.     Mch. 

10,  1898. 

4.  Welles,  A.  M.     The  Castlewood  Dam.     Eng.  Rec.     Dec.  24,  1898.     Vol.  39, 

p.  69. 

5.  Hardesty,  W.  P.     The  Castlewood  Rock-fill  Dam  and  the  Canal  of  the 

Denver  Land  &  Water  Co.     Eng.  &  Min.  Jour.     Feb.  9,  1899. 

6.  Parker,  H.  S.     East  Canyon  Creek  Dam,  Utah.     Eng.  Rec.     Sept.  2,  1899. 

7.  Dumas,  A.    Rock  Dams  with  Metallic  Reinforcement.     Genie  Civil.     Oct, 

21,  1899. 

8.  The  Goose  Neck  Canyon  Dam.     Eng.  Rec.     Mch.  10,  1900. 

9.  The  Cascade  Rock-fill  on  the  Erie  R.  R.     Eng.  News.     Dec.  27,  1900,  vol. 

44,  p.  440. 

10.  Hardesty,  W.  P.     A  Rock-fill  Dam  with  Steel  Core  Across  East  Canyon 

Creek,  Utah.     Eng.  News.     Jan.  2,  1902. 

11.  Reconstruction  of  the  Castlewood   Dam.     Eng.   Rec.     July   12,   1902. 

12.  The  Plant  of  the  Pikes  Peak  Power  Co.     Eng.  Rec.     July  19,  1902. 

13.  Lake  McMillan  Dam,  Pecos  River,  N.  M.     Eng.  Rec.     June  9,  1894. 

MASONKY  DAMS. 

1.  Ashhurst,  F.  H.     Reconstruction  of  the  Bhim  Tal  Dam,  Kumaon,  India. 

Proc.  Inst.  C.  E.  vol.  75,  p.  202.     1884. 

2.  Hill,  John  W.     A  Masonry  Dam.     Trans.  Am.  Soc.  C.  E.  June,  1887. 

3.  Tonsa  Dam,  Bombay  Water  Works.    Eng.  News.    June  30,  1892,  pp.  646-7. 

Eng.  Rec.     Dec.  19,  1891,  p.  40. 

4.  New  Croton  Dam  for  the  New  York  Water  Supply.     Eng.  News.     June  2, 

1892,  pp.  552-3.     R.  R.  Gaz.     Oct.  14,  1892.     p.  163. 

5.  Folsom  Dam  at  Folsom,  Cal.     R.  R.  &  Eng.  Jour.     July,  1892.     pp.  315-8. 

6.  Vyrnwy  Dam  for  the  Liverpool  Water  Works,  England.     R.  R.  &  Eng. 

Jour.     Sept.  1892. 


598  Principles  of  Construction  of  Dams. 

7.  Concrete   Masonry   Dam   of   the   Butte   City  Water   Company,    Montana, 

Eng.  News,  Dec.  15,  22,  1892,  pp.  554  &  584. 

8.  Periar   Concrete    Dam    in.   India   for    Irrigation    Purposes.     Lon.    Engr. 

Nov.  25,  Dec.  2,  9,  1892.     Eng.  Rec.     Dec.  31,  1892,  pp.  92-3. 

9.  Report  of  the  Austin  Board  of  Public  Works,  Austin,  Texas.     Eng.  News 

Jan.  26,  1893,  pp.  88-90. 

10.  Dam  at  Austin,  Texas.     Eng.  News.     Jan.  26,  1893,  pp.  87-88. 

11.  McCulloh,  Walter.     Sodom  Dam,  New.  York.    Trans.  Am.  Soc.  C.  E.    Mch.. 

1893,  vol.  28,  pp.  185-199.     Discussion  by  Members  of  Society. 
Trans.  Am.  Soc.  C.  E.     May,  1893,  vol.  28,  pp.  348-351. 

12.  McCulloh,   Walter.     The   Construction   of   a   Water   Tight    Dam.     Trans. 

Am.  Soc.  C.  E.     Apr.  1893. 

13.  Basin  Creek  Dam  for  Water-Works  of  Butte,  Mont.     Eng.  News.     Aug.  17,. 

1893,  p.  130. 

14.  Dam  5  of  the  Stone  Brook  Portion  of  the  Boston  Water  Works.     Eng. 

Rec.     Nov.  4,  1893,  p.  361. 

15.  Bettes,  Stockwell.     Determining  Minimum  Section  for  Overfall  Masonry 

Dams.     Eng.  News.     Dec.  28,  1893,  vol.  30,  p.  511. 

16.  Masonry   Dam   at   LaGrange,   Gal.     Eng.    News.     March   29,    1894.     Eng. 

Rec.     March  3,  1894. 

17.  Pellitveau,  Albert.     Great  Masonry  Dam.    Ann.  des  Fonts  et  Chaussees. 

May,  1894. 

18.  Masonry  Dam,  Chemnitz  Water  Works,  Germany.     Eng.  Rec.     July  28r 

1894,  Jour,  f  Gasb.  u  Wasserv.     Sept.  1,  1894.     Sci.  Am.   Sup. 
Nov.  10,  1894. 

19.  Snyder,  F.  E.     The  Colorado  River  Dam  at  Austin,  Texas.     Eng.  News. 

Aug.  2,  1894.     Eng.  Mag.     Nov.  1894. 

20.  Dunning's  Dam.     Eng.  News.     Oct.  18,  1894.     Eng.  Rec.     Oct.   20,   1894, 

21.  Gould,  E.  S.     The  Dunning's  Dam,  Partly  of  Earth  and  Partly  of  Ma- 

sonry.    Trans.  Am.  Soc.  C.  E.     Nov.  1894. 

22.  New  Masonry  Dam  at  Lonsdale,  R.  I.     Eng.  News,  Mar.  14,  1895. 

23.  Van  Buren,  John  D.     High  Masonry  Dams.     Trans.  Am.  Soc.  C.  E.  voL 

34,  No.  6,  pp.  495-520.     1895. 

24.  Haller,  Prof.    The  Bouzey  Dam.  Jour.  f.   Gasb.   u.  Wasserv.     June   22, 

1895,  et  seq. 

25.  Overflow  of  the  Sweetwater  Dam.     Eng.  News.     Aug.  15,  1895,  vol.   34r 

p.  111. 

26.  Marstrand,  O.  J.     Curved  Masonry  Dam  for  Water  Works  of  Remscheid, 

Germany.     Eng.  News.     Jan.  30,  1896. 

27.  Firth,  Charles.     Concrete  Dams  on  the  Coosa  River,  Ala.     Eng.  News, 

Feb.  20,  1896. 

28.  Savage,  H.  N.     Repair  and  Extension  of  the  Sweetwater  Dam.     Eng.  Rec. 

March  12,  1896. 

29.  The  Cold  Spring,  N.  Y.,  Concrete  Dam.     Eng.  Rec.     July  11,  1896. 

30.  Remscheid  and  Chemintz  Water  Works.     Eng.,  Lond.     July  31,  1896. 

31.  New  Arched  Dam  at  Nashua,  N.  H.     Eng.  Rec.     Aug.  8,  1896. 

32.  Dahl,  H.  M.  T.     A  New  Dam  at  Minneapolis.     Eng's.  Year  Book  Univ.  of 

Minn.,  1897. 


Literature.  599 

33.  The  Proposed  Steel-Faced  Concrete  Arch  Dam,  Ogden,  Utah.     Eng.  Rec. 

Mch.  6,  1897. 

34.  Thompson,    Sanford   E.     The   New    Holyoke   Water   Power    Dam.     Eng. 

News.     May  13,  1897. 

35.  Homey,  Odus  C.     Concrete  Water  Power  Dam  at  Rock  Island  ArsenaL 

Jour.  W.  Soc.  Engs.     June,  1897. 

36.  Schuyler,  James  D.     The  Construction  of  the  Hemet  Dam.     Jour.  Assn. 

Engng.  Socs.     Sept.  1897. 

37.  Schuyler,   James  D.     The  Hemet  Irrigating  Dam.     Sci.   Am.     Sept.   25_ 

1897. 

38.  The  Muchkundi  Dam.     Engr.  Lond.     Oct.  22,  1897. 

39.  The  Hemet  Dam.     Eng.  News.     March  24,  1898. 

40.  Richter,  Irving.     An  Unusual  Small  Masonry  Dam.     Eng.  Rec.     Nov.  26,, 

1898. 

41.  Rafter,  G.  W.,  Greenlach,  W.,  Horton,  R.   E.     The   Indian   River   Dam. 

Eng.  News.     May  8,  1899. 

42.  Crosby,  W.   O.     Geology  of  the  Wachusett  Dam  and  Aqueduct  Tunnel. 

Tech.  Quar.     June,  1899. 

43.  The  New  Masonry  Dam  at  Holyoke.     Eng.  Rec.     July. 22,  1899. 

44.  Gould,  E.  S.     Earth  Backing  for  Masonry  Dams.     Eng.  Rec.     Dec.   23r 

1899. 

45.  The  Bear  Valley  Dam  as  an  Arch.     San  Bernardino  Co.,  Cal.    Techno- 

graph  No.  14,  1899-1900. 

46.  The  Tariffville  Plant  Plans  of  Hartford  Elec.  Light  Company.     Etig.  Rec. 

Mch.  24,  1900. 

47.  The  New  Water  Poweir  of  the  Hartford  Electric  Light  Co.     Am.  Electri- 

cian.    Mch.  1900. 

48.  Flinn,  Alfred  D.     The  Wachusett  Dam.     Eng.  News.     Sept  13.  1900. 

49.  The  Wachusett  Dam.     Eng.  Rec.     Sept.  8,  1900. 

50.  A  Concrete'  Power  Dam  at  Middle  Falls,  N.  Y.     Eng.  Rec.     Oct.  4  1900. 

51.  Stewart,  J.  A.     Building  of  the  Great  Wachusett  Dam.     Sci.  Am.   Sup. 

Dec.  15,  1900. 

52.  The  Dam  &  Power  Station  of  The  Hudson  River  Power  Company.     Eng. 

Rec.     Mar.  8,  1902. 

53.  Heaman,  J.  A.     Description  of  a  Dam  and  Accompanying  Work  Built  for 

the  Water  Commissioners.     Can.   Soc.  of  Civ.  Engrs.     Apr.  24,. 
1902. 

54.  A  Concrete  Dam  Near  London,  Ontario.     Eng.  Rec.     July  26,  1902. 

55.  Frechl,  H.     Construction  of  the  Lauchenesee/  Dam.     Eng.  Rec.     Aug.  30,. 

1902. 

56.  The  Spier's  Falls   Dam  of  The  Hudson  River  Water  Power  Company. 

E"ng.  News.     June  18,  1903. 

57.  Morton,  Walter  Scott.    A  New  Water  Power  Development  at  New  Mil- 

ford,  Conn.     Eng.  Rec.     Feb.  13  and  20,  1904. 

58.  Harrison,  Chas.  L.,  and  Woodard,  S.  H.     Lake  Cheesman  Dam  and  Res- 

ervoir.    Proc.  Am.  Soc.  C.  E.     Aug.  1904. 

59.  Galliot,    M.     Reinforcement   of   the   Grosbois    Dam.     Ann.    des   Fonts    et 

Chaussees,  1905.' 


6oo  Principles  of  Construction  of  Dams. 

60.  The  Roosevelt  Masonry  Dam  on  Salt  River,  Arizona.     Eng.  News.     Jan. 

12,  1905. 

61.  A  Quickly  Erected  Reinforced  Concrete  Dam  at  Fenelon  Falls,  Ont.     Eng. 

News.     Feb.  9,  1905. 

62.  A  Concrete  Dam  on  a  Pile  Foundation  at  St.  John's  Lake,  Long  Island, 

N.  Y.     Eng.  News.     Feb.  9,  1905. 

63.  Guarini,  Emile.     Barossa  Dam,  Southern  Australia.     Sci.  Am.     April  1, 

1905. 

64.  Hollow  Reinforced  Concrete  Dam  at   Schuylerville,   N.  Y.     Eng.   News. 

April  27,  1905. 

65.  Blodgett,    Geo.    W.    -The    Wachusett    Dam    of    the    Metropolitan    Water 

Works.     R.  R.  Gaz.,  vol.  39,  p.  100.     Aug.  4,  1905. 

66.  Dams  for  the  New  Plant  of  the  United  Shoe  Machinery  Company,  Bev- 

erly, Mass.     Eng.  Rec.     Sept.  2,  1905. 

67.  Shedd,  Geo.  G.     The  Garvin's  Falls  Dam,  Canal  and  Hydro-Electric  Plant. 

Jour.  Assn.  E'ng.  Soc.     Oct.  1905. 

68.  Gowen,  Chas.  S.     Changes  at  the  New  Croton  Dam.     Proc.  Am.  Soc.  C.  E. 

Mch.  1906. 

69.  The  Pedlar  River  Concrete  Block  Dam.     Lynchburg  W.  Wks.     Eng.  Rec. 

May  12,  1906. 

70.  The  Stresses  on   Masonry  Dams.     Editorial  Review   of  Paper   by  Prof. 

Carl  Pearson.     Engineering,  London,  September,  1907. 

71.  The  McCall's  Ferry  Hydraulic  Electric  Power  Plant.     Eng.  News,  Sep- 

tember 12,  1907. 

TIMBER    DAMS. 

1.  Parker,   M.    S.     Black  Eagle  Falls   Dam   at   Great   Falls,   Mont.     Trans. 

Am.  Soc.  C.  E.     July,  1890,  vol.  27,  pp.  56-59.     Eng.  Rec.     Oct.  8, 
1892,  p.  295. 

2.  Sewell   Falls  Dam  Across  Merrimac  River,  near  Concord,  N.   H.     Eng. 

News.     April  19,  1894. 

3.  Parsons,  G.  W.     Closing  the  Timber  &  Stone  Dam  at  Bangor,  Me.     Eng. 

News.     July  26,  1894. 

4.  Brown,  Robert  Gilman.     Additions  to  the  Power  Plant  of  the  Standard 

Consolidated  Mining  Company.     Trans.  Am.  Inst.  Mining  Engrs. 
Sept.  1896. 

5.  Ripley,  Theron  M.     The  Canyon  Ferry  Dam,  Canyon  Ferry,  Mont.     Jour. 

Assn.  Engng.  Soc.     May,  1898. 

6.  The  Butte,  Montana,  Power  Plant.     Eng.  Rec.     Mch.  5,  1898. 

7.  Carroll,  Eugene.     Construction  of  a  Crib  Dam  for  Butte  City  Water  Co., 

Butte,  Montana.     Jour.  Assn.  Engng.  Soc.     April,  1899. 

8.  The   Reconstructed   Canyon    Ferry    Dam,   near    Helena,    Montana.     Eng. 

News.     Apr.  26,  1900. 

9.  A  Large  Crib  Dam.     Butte,  Mont.     Eng.  Rec.     Feb.   3,  1900. 

10.  Harper,  Jos.  H.     The  Reconstruction  of  Big  Hole  Dam,  Big  Hole,  Mon- 
tana.    Jour.  Assn.  of  Engng.  Soc.     Apr.  1900. 


Literature.  601 

11.  Tower,  G.  W.     Timber  Dam  at  Outlet  of  Chesuncook  Lake,  Penobscot 

River.     Eng.  News.     Sept.  1,  1904. 

12.  Woermann,  J.  W.     A  Low  Crib  Dam  Across  the  Rock  River. 

STEEL  DAMS. 

1.  Fielding,  John  S.     The  Use  of  Steel  in  the  Construction  of  Dams.     Can. 

Arch.     Aug.  1897. 

2.  Steel  Weir,  Ash  Fork,  Arizona.     Eng.  Rec.     Apr.  9,  1898. 

3.  Steel  Dam  at  Ash  Fork,  Arizona.     Eng.  News.     May  12,  1898. 

4.  Fielding,  John  S.     Proposed  Design  for  a  Steel  and  Concrete  Dam.     Eng. 

News.     Nov.  16,  1899. 

5.  Bainbridge,  F.  H.     Structural  Steel  Dams.     Jour.  West.  Soc.  Eng.     1905. 

6.  The  Hauser  Lake  Steel  Dam  in  the  Missouri  River  Near  Helena,  Mont. 

Eng.  New.     Nov.  14,  1907. 

7.  Wheeler,  J.  C.     A  Collapsibe  Steel  Dam  Crest.     Eng.  News.     October  3. 

1907. 

REINFORCED    CONCRETE    DAMS. 

1.  A   Large   Reinforced   Concrete   Dam   at   Ellsworth,    Maine.     Eng.    News. 

May,  1907. 

2.  A  Hollow  Reinforced  Concrete  Dam  at  Theresa,  New  York.     Eng.  News, 

Nov.  5,  1903. 

3.  Reinforced  Concrete  Dam  at  Schuylerville,  New  York.     Eng.  News,  April 

27,  1905. 

4.  A  Concrete  Steel  Dam  at  Danville,  Kentucky.     Eng.  Rec.     Dec.  3,  1904. 

5.  Reinforced  Concrete  Dam  at  Feneloni  Falls,  Ontario.     Eng.  News,  Feb.  9, 

1905. 

DAM    FAILURES. 

1.  Washout  at  the  Pecos  Dam.     Eng.  Rec.     Aug.  26,  1893. 

2.  Failure  of  the  Bouzey  Reservoir  Dam.     Lon.  Engr.,  May  3,  1895,  p.  583; 

Eng.  News,  May  9,  1895,  p.  312;    Lon.  Engr.,  May  31,  1895,  p. 
383;  Eng.  News,  May  23,  1895,  p.  332. 

3.  Catastrophe  at  Lima,  Montana.     Irrigation  Age,  July,  1894. 

4.  Rickey,  J.  U.     Failure  of  Dam  at  Minneapolis,  Due  to  Previous  Weaken- 

ing Through  Ice  Pressure.     Eng.  News,  May  11,  1899. 

5.  Failure  of  Masonry  Dams.     Annales  des  Ponts  et  Chaussees,  vol.  7,  No.  7, 

pp.  77-89    (1895). 

6.  The  Johnstown  Disaster.     Eng.  News,  June  18,  1899. 

7.  Recent   Events   at   the   Castlewood    Dam,   Castlewood,   Colo.     Eng.    Rec. 

May  19,  1900. 

8.  The  Failure  of  Two  Earth  Dams  at  Providence,  R.  I.     Eng.  News,  Mch. 

12,  1901. 

9.  Destruction  of  Dams  in  the  South.     Eng.  Rec.     Jan.  11,  1902. 

10.  The  Failure  of  the  Dam  of  the  Columbus  Power  Company  at  Columbus, 
Ga.     Eng.  News,  Jan.  23,  1902. 


602  Principles  of  Construction  of  Dams. 

11.  Failure  of  the  Lower  Tallassee  Dam  at  Tallassee,  La.     Eng.  News,  Feb. 

13,  1902. 

12.  Johnson,  Robert  L.     Some  Thoughts  Suggested  by  the  Recent  Failure 

of  Dams  in  the  South.     Eng.  News,  Mch  20,  1902. 

13.  Hill,  W.  R.    A  List  of  Failures  of  American  Dams.     Eng.  Rec.     Sept.  27, 

1902. 

14.  The  Break  in  the  Utica  Reservoir.     Eng.  Rec.     Sept.  27,  1902. 

15.  Whited,  Willis.     The  Failure  of  the  Oakford  Park  and  Fort  Pitt  Dam. 

Eng.  News,  July  23,  1903. 

16.  Robinson,  H.  F.     Construction,  Repairs  and  Subsequent  Partial  Destruc- 

tion of  Arizona  Canal  Dam.     Eng.  News,  Apr.  27,  1905. 

17.  Murphy,  E.  C.     Failure  of  Lake  Avalon  Dam,  near  Carlsbad,  N.  H.     Eng. 

News,  July  6,  1905. 


CHAPTER  XXV. 

APPENDAGES  TO  DAMS. 

305.  Movable  Dams. — The  height  of  a  dam  is  limited  in  the  man- 
tier  hereinbefore  described.  It  will  be  noted  that  the  limit  is  that 
imposed  by  high  water  conditions  and  that,  as  a  rule,  the  water  sur- 
face during  low  stages  could  be  raised  to  a  considerable  amount 
without  interference  with  the  riparian  owners,  if  at  the  same  time 
flood  conditions  could  be  provided  for.  In  order  to  provide  such 
•conditions,  movable  dams  are  sometimes  constructed  which  will 
permit  of  raising  or  lowering  all  or  a  part  of  the  structure  as  the 


.  368. — U.  S.  Movable  Dam  on  Pile  Foundation,  McMechen,  W.  Va. 
News,  vol.  54,  page  100.) 


(Bng. 


stage  of  the  water  requires.  These  flexible  portions  of  the  dam 
may  consist  of  a  gate  or  series  of  gates  which  can  be  raised  or 
lowered.  Sometimes  a  considerable  portion  of  the  dam  is  made 
flexible  by  the  construction  of  a  bear  trap  leaf,  which  is  usually 
raised  and  lowered  by  hydraulic  pressure,  and  by  means  of  which 
the  head  of  water  can  be  readily  and  rapidly  controlled.  Sometimes 


604 


Appendages  to  Dams. 


Movable  Dams. 


the  entire  dam  is  made  movable  by  the  use  of  Chanoine  wickets 
(see  Fig.  368)  and  similar  types  of  dams,  a  part  of  which  may  be 
removable  while  other  parts  are  folded  down  on  the  bed  of  the 
stream,  allowing  the  flood  waters  to  pass  over  them.  Most  of  such 


i  a  -  o    — 


Fig.  370.— Tainter  Gates  for  Morris  Plant,  Economy  Light  and  Power  Co. 

constructions  are  expensive  and  are  used  most  largely  on  govern- 
ment works  for  the  control  of  rivers  for  navigation  purposes. 

The  objection  to  movable  dams  for  water  power  purposes  is 
that  the  reduction  in  the  elevation  of  the  head  water  by  their  use 
commonly  so  reduces  or  destroys  the  head  that  the  continuity  of  the 

37  4 


6o6 


Appendages  to  Dams. 


power  output  is  interrupted.  The  same  objection  also  applies  to 
any  gate,  flash  board  or  other  device  designed  to  reduce  the  head. 
Such  reduction  is  usually  made  during  conditions  of  flow  under 
which  the  natural  head  that  would  obtain  is  already  at  a  minimum. 
306.  Flood  Gates. — Flood  gates  are  quite  commonly  used  in 
water  power  dams  to  control  or  modify  extreme  flood  heights. 
These  gates  are  commonly  designed  to  be  raised  so  as  to  permit  of 
the  escape  of  the  water  underneath  them.  The  tainter  gate,  in 


Fig.  371.' — Hoist  for  Tainter  Gates  of  Northern  Hydro  Electric  Power  Co. 

some  of  its  modifications,  is  perhaps  most  widely  used  for  this  pur- 
pose. Fig.  369  shows  a  plan,  elevation  and  section  of  a  tainter 
gate,  designed  by  L.  L.  Wheeler,  resident  engineer  of  the  Illinois 
and  Mississippi  Canal,  for  the  U.  S.  Government  dam  at  Sterling, 
Illinois.  This  is  one  of  a  series  of  tainter  gates  designed  for  the 
flood  control  of  the  Rock  River  at  that  point.  The  gates  are  oper- 
ated by  an  overhead  hoist  which  can  be  moved  from  gate  to  gate 
when  it  is  desired  to  manipulate  them. 

Fig.  37°  is  a  section  of  one  of  six  gates  designed  by  the  writer 
for  the  Morris  plant  of  the  Economy  Light  and  Power  Company. 


Flood  Gates. 


607 


Fig.  372. — Tainter  Gates  at  Upper  U.  S.  Gov.  Dam,  Appleton,  Wis. 


Fig.  373. — Tainter  Gates  at  Lower  U.  S.  Gov.  Dam,  Appleton,  Wis. 


6oS 


Appendages  to  Dams. 


Flashboards. 


609 


These  gates  are  operated  by  a  movable  hoist,  similar  to  Fig.  371, 
•which  travels  on  a  track  on  the  bridge  above. 

Figs.  372  and  373  are  views  of  the  steel  tainter  gates  constructed 
in  the  upper  and  lower  U.  S.  Government  dams  across  the  Fox 
River  at  Appleton,  Wisconsin. 

In  the  dam  of  the  Southern  Wisconsin  Power  Company  at  Kil- 
"bourn,  Wisconsin,  the  rise  of  the  flood  water  is  so  great  (about  16 
feet)  that  it  was  found  impracticable  to  construct  lift  gates  to  re- 
duce the  flood  heights.  In  this  case  the  writer  has  divided  the  crest, 


Fig.  375.— Flash  Boards  and  Supports,  Rockford  Water  Power  Co. 

"by  piers,  into  twelve  sctions.  Between  each  two  piers  a  twenty- 
Jive  foot  gate  is  placed  (see  Fig.  374)  which  can  be  lowered  into  the 
dam  six  feet,  thus  reducing  the  extreme  flood  height  by  that  amount. 
These  gates  are  of  steel  and  weigh  about  seven  tons  each.  They 
may  be  operated  by  an  electric  motor  or  may  be  manipulated  by 
hand,  should  occasion  require. 

307.  Flashboards. — The  control  of  limited  variations  in  head  is 
-commonly  accomplished  by  means  of  flash-boards  which  are  widely 
-used  for  this  purpose.  The  simplest  form  of  flash-board  consists 


6io 


Appendages  to  Dams. 


of  a  line  of  boards  placed  on  the  crest  of  the  dam  (see  Fig.  375) 
usually  held  in  place  by  iron  pins  to  which  the  boards  are  com- 
monly attached  by  staples.  The  object  of  flash-boards  is  princi- 
pally to  afford  a  certain  pondage  to  carry  the  surplus  water  from 
the  time  of  minimum  use  of  power  to  the  time  of  maximum  demand. 
Incidentally,  the  head  is  raised  and  the  power  is  also  increased  in 
this  way.  The  supports  of  the  flashboards  should  be  so  arranged 
that  they  will  withstand  only  a  comparatively  low  head  of  water 
flowing  over  the  boards,  and  will  be  carried  away  if  a  sudden 


Fig.    376. — Automatic    Drop-Shutter    for    Betiva    Dam,    India.     (Eng.    News, 

June  4,  1903.) 

flood  should  raise  the  head  materially  above  a  safe  elevation.  If 
the  boards  are  so  supported  as  to  withstand  the  discharge  of  heavy 
floods,  they  will  form  a  permanent  portion  of  the  dam  and  increase 
its  fixed  elevation  to  such  an  extent  as  to  create  damage  which  their 
use  is  supposed  to  avoid.  Sometimes  the  pins  supporting  the 
boards  are  made  so  light  that  they  must  be  held  in  position  by  in- 
clined braces.  These  braces  are  sometimes  supplied  with  steel 
eye-bolts  through  which  is  passed  a  cable.  A  large  steel  washer 
is  attached  at  one  end  and  a  winding  drum  at  the  other.  (See  Fig. 
3/5).  Commonly,  if  a  flood  is  anticipated,  the  boards  are  removed 
and  stored  for  future  use.  If,  however,  a  sudden  flood  should  arise, 
the  inclined  braces  are  removed  by  winding  up  the  cable  and 
the  pressure  on  the  flash-boards  bends  the  pins  and  the  boards 
are  washed  away.  The  expense  involved  by  the  loss  of  flash-boards. 


Head  Gates  and  Head  Gate  Hoists. 


611 


is  not  excessive  as  one  set  will  commonly  take  care  of  the  entire 
summer  low  water  period.  The  expense  involved  in  their  use  is 
therefore  only  the  cost  of  one  set  of  flash-boards  per  year. 

Sometimes  the  flash-boards  constitute  a  permanent  but  adjust- 
able part  of  the  dam  and  are  lowered  automatically  during  stages 
of  high  water.  (See  Fig.  376).  On  some  dams,  especially  at 
waste  weirs  of  canals  and  reservoirs  where  the  fluctuations  in 
height  are  inconsiderable,  the  dam  may  be  provided  with  a  foot 
bridge  which  makes  the  whole  crest  of  the  dam  accessible  at  all 
times  arid  from  which  the  flash-boards  can  be  readily  adjusted. 
This  plan  is  used  on  the  dam  across  the  Chippewa  River  at  Eau 


Fig.  377.— Adjustable  Flash  Boards  at  Eau  Claire,  Wis. 

Claire,  although  this  river  is  subject  to  high  floods.  (See  Fig.  377). 
Ordinarily,  on  rivers  subject  to  such  conditions,  this  type  of  con- 
struction is  impracticable. 

In  some  dams,  instead  of  gates  or  flash-boards,  vertical  stop 
planks  or  needles  are  used.  These  consist  of  planks  or  squared 
timbers  that  are  lowered  vertically  into  position,  stopping  off  the 
opening  partially  or  wholly,  as  desired.  They  are  commonly  sup- 
ported by  a  shoulder  at  the  bottom  of  the  opening  and  one  or  more 
cross  beams  above. 

308.  Head  Gates  and  Head  Gate  Hoists, — It  is  usually  desirable 
to  control  the  water  at  the  inlets  to  the  headrace  by  the  use  of  gates 
which  may  be  closed  in  emergencies  or  for  the  purpose  of  making 


6l2 


Appendages  to  Dams. 


Head  Gates  and  Head  Gate  Hoists. 


614  Appendages  to  Dams. 

necessary  repairs  or  modifications  in  the  raceway  through  which 
the  water  is  diverted  to  the  plant.  In  northern  rivers  it  is  also 
found  desirable  to  prevent  the  entrance  of  ice  into  the  raceway 
either  by  the  construction  of  a  floating  or  fixed  boom  in  front  of  the 
gates  or  by  constructing  a  system  of  submerged  arches  either  in 
front  of,  or  as  a  part  of,  the  gateways.  By  means  of  such  construc- 
tion the  floating  ice  or  other  floating  material  may  be  diverted  from 
the  raceway  and  passed  over  the  spillway  of  the  dam. 

The  head  gates  must  be  sufficiently,  substantial  to  allow  the  race 
to  be  emptied  under  ordinary  conditions  of  water  and  to  protect 
the  raceway  under  flood  conditions. 

Fig.  378  shows  an  elevation  of  the  head  gates,  designed  by  the 
writer  for  the  power  plant  at  Constantine,  Michigan.  These  are 
shown  in  detail  !by  Fig.  379.  A  rear  view  of  these  gates  from  the 
race  side  is  also  shown  in  Fig.  380.  These  gates  are  double  wooden 
gates  with  concrete  gateways  and  are  arched  over  between  the 
piers  so  as  to  permit  the  passage  of  men  and  teams.  These  gates 
are  designed  to  pass  about  2,000  cubic  feet  per  second. 

Fig.  381  shows  a  set  of  double  wooden  gates,  the  posts  and  braces 
of  which  are  made  of  structural  steel  designed  by  the  writer  for  the 
power  plant  of  Mr.  Wait  Talcott,  at  Rockford,  Illinois. 

In  the  Constantine  gates  the  gate  mechanism  is  geared  for  fairly 
rapid  operation  by  two  men.  The  Rockford  gate  apparatus  is  very 
simple,  the  gate  being  handled  with  a  capstan  bar  by  a  single  man 
but  at  a  much  slower  speed. 

Fig.  382  shows  the  movable  head  gate  hoist  designed  b'y  the 
writer  for  the  operation  of  the  head  gates  at  the  Kilbourn  plant  of 
the  Southern  Wisconsin  Power  Company. 

309.  Fish-Ways. — In  almost  every  state  fishways  are  required  by 
law  in  any  dam  constructed  on  natural  waterways.  These  fish- 
ways  must  be  so  arranged  as  to  permit  the  free  passage  of  fish  up 
the  stream. 

Fig.  383  shows  a  concrete  fishway  built  by  the  writer  in  con- 
nection with  the  ogee  concrete  dam  constructed  across  the  Ver- 
million  River  at  Danville,  Illinois.  Fig.  384  is  a  fishway  designed 
by  Mr.  L.  L.  Wheeler  and  constructed  in  the  dam  at  Sterling,  Illi- 
nois. The  Sterling  dam  is  a  timber  crib  dam  and  the  fishway  is 
constructed  of  timber.  Fig.  385  shows  the  type  of  fishway  recom- 
mended by  the  Fish  Commission  of  the  State  of  Wisconsin  and 
ordinarily  used  in  that  state. 


Head  Gates  and  Head  Gate  Hoists. 


615 


o 

00 

CO 

bo 


6i6 


Appendages  to  Dams. 


Head  Gates  and  Head  Gate  Hoists. 


617 


Fig.  382.— Head  Gate  Hoist,  Kilbourn,  Wis.  (Southern  Wisconsin  Power  Co.). 

The  purpose  of  these  fishways  is  to  afford  a  gradual  incline 
through  which  a  continuous  stream  of  water  of  comparatively  low 
velocity  shall  flow  and  against  which  the  fish  may  readily  swim. 
Both  the  inlet  and  outlet  should  be  below  low-water  and  the  out- 
let should  be  in  such  a  position  that  the  fish,  when  they  ascend  the 
stream  and  reach  the  dam,  in  passing  from  one  side  to  the  other  in 
searching  for  a  passage,  are  naturally  led  to  the  point  where  the 


6i8 


Appendages  to  Dams. 


Fish  ways. 


619 


Fig.  384. — Timber  Fishway  in  Dam  at  Sterling,  111.     (Eng.  News.) 


Fig.  385. — Fishway  of  Fish  Commission,  State  of  Wisconsin. 


620 


Appendages  to  Dams. 


flowing  water  is  encountered.  The  slope  of  these  fishways  should 
not  be  steeper  than  one  vertical  to  four  horizontal,  and  the  water 
should  be  so  deflected  that  the  velocity  will  be  reduced  as  low  as 
possible.  A  fishway  should  be  entirely  automatic  and  free  from 
all  regulating  devices.  It  is  usually  desirable  for  the  openings  in 


EL  Fit  933 


SPIL  LWAY  SECTION. 


PLAN 


SECTION    THROUGH    LO&-SLUICE 


Fig.  386. — Log  Way  in  the  Chesuncook  Timber  Dam.     (Eng.  Rec.,  vol.   50, 

p.  70.) 

the  bulkheads  or  baffles  to  increase  progressively  from  the  lower 
to  the  upper  one  in  order  to  insure  that  the  passage  of  the  fishway 
shall  be  full  of  water.  The  fishway  should  be  so  covered  as  to  pre- 
vent interference,  but  must  be  light  or  it  will  not  be  used  by  the 
fish. 


Log-Ways. 


621 


310.  Log- Ways. — The  free  navigation  of  streams  for  logging 
purposes  is  provided  by  law  in  most  states  and  it  is  therefore  neces- 
sary where  logging  is  practiced  to  provide  ready  means  for  their 
passage  over  or  through  the  dam.  This  is  accomplished  in  the 


Fig.  387. — Log  Way  at  Lower  Dam,  Minneapolis,  Minn. 

Kilbourn  dam  (see  Fig.  374)  by  the  lowering  of  any  one  of  the 
flood  gates. 

Fig.  386  shows  a  plan  and  section  of  the  log-sluice  constructed  in 
the  Chesuncook  timber  dam  on  the  Penobscot  River.  A  section  of 
the  spillway  of  the  dam  is  also  shown  in  the  same  figure. 

Fig.  387  is  a  view  of  the  logway  in  the  lower  dam  at  Minneapolis. 
This  sluice  is  only  six  or  eight  feet  in  width,  and  the  depth  and 
quantity  of  water  flowing  is  controlled  by  a  bear  trap  leaf. 


622  Appendages  to  Dams. 

In  most  cases,  to  avoid  an  excessive  waste  of  water,  it  is  desir- 
able to  build  the  logway  as  narrow  as  possible.  Under  such  condi- 
tions it  becomes  necessary  to  guide  the  logs  into  the  sluice  by  tim- 
ber booms  which,  leaving  the  sluice  at  a  law  angle,  are  strung  up- 
stream to  such  points  that  the  logs  in  floating  down  stream  shall 
enter  between  them  and  be  guided  to  the  sluice  opening. 


LITERATURE. 

MOVABLE    DAMS,    FLASHBOABDS,    ETC. 

1.  Harcourt,  L.  V.     Fixed  and  Movable  Weirs.     Proc.  Ins.   C.   E.     Vol.  60, 

p.  24.     Jan.  1880. 

2.  Chittenden,  Hiram  M.     American  Types  of  Movable  Dams.     Eng.  News, 

Feb.  7,  1895.     Vol.  33,  p.  84. 

3.  Stickney,  Amos.     Lifting  Dam.     Jour.  Assn.  Ehg.  Soc.     Vol.  16,  p.   255. 

June,  1896. 

4.  Thomas,  B.  F.    A  Design  for  a  Movable  Dam.     Jour.  Assn.  Eng.   Soc. 

Vol.  16,  p.  260.     June,  1896. 

5.  Chittenden,   H.   M.     Modified   Drum  Weir.     Jour.   Assn.   Eng.    Soc.     Vol. 

16,  p.  249.     June,  1896. 

6.  Powell,  Archibald  0.     Movable  Dams,  Sluice  and  Lock  Gates  of  the  Bear- 

Trap  Type.     Jour.  Assn.  Eng.  Soc.     Vol.  16,  p.  177.     June,  1896. 

7.  Marshall,   W.    L.     Marshall's    Bear-Trap    Dams.     Jour.    Assn.    Eng.    Soc. 

Vol.  16,  p.  218.     June,  1896. 

8.  Jones,  W.  A.     Bear-Trap  Weirs.^   Jour.  Assn.  Eng.  Soc.     Vol.  16,  p.  238. 

June,  1896. 

9.  Johnson,  Archibald.     Bear-Trap  Gates  in  the  Navigable  Pass,  Sandy  Lake 

Reservoir  Dam,  Minnesota.     Jour.  Assn.  of  Eng.  Soc.     Vol.  16, 
p.  210.     June,  1896. 

10.  Martin,  Wm.     Bear-Trap  Gate  in  Davis  Island  Dam,  Ohio  River.     Jour. 

Asso.  Eng.  Soc.     Vol.  16,  p.  208.     June,  1896. 

11.  Movable  Dams  on  the  Great  Kanawha  River.     Eng.  News,  vol.  36,  p.  426. 

Dec.  31,  1896. 

12.  Needle  Dams.     Ann.  des  Fonts  et  Chaussees.     Part  II.     1897. 

13.  Bear-Trap  Dam.     Chicago  Drainage  Canal.     R.  R.  Gaz.     Feb.  12,  1897. 

14.  The  Use  o£  Rolling  Shutters  in  Movable  Dams.    Genie  Civil.    May  1,  1897. 

15.  Larminie,   J.   C.     Falling   Shutters,    Godavery,   Anient.     Ind.   Eng.     Dec. 

18,  1897. 

16.  Thomas,  B.  F.     Movable  Dams.     Trans.  Am.  Soc.  C.  E.     Vol.  39,  p.  431. 

Mar  1898. 

17.  Bear-.Trap  Dam  for  Regulating  Works,  Chicago  Drainage  Canal.     Eng. 

News.     Mar.  24,  1898. 

18.  The  Movable  Dam  on  the  Big  Sandy  River.     Genie  Civil.     May  14,  1898. 

19.  Marshall  Automatic  Movable  Dam.     Eng.  News.     May  26,  1898. 


Literature.  623 

20.  The  Management  of  Non-parallel  Motion  and  Deficient  Operating  Head 

in    Bear-Trap    Dams    by    Auxiliary    Constructions.     Eng.    News, 
May  26,  1898. 

21.  New  United  States  Government  Needle  Dam  at  Louisa,  Kentucky,  on  the 

Big  Sandy  River.     Eng.  News,  vol.  40,  p.  2.     July  7,  1898. 

22.  The  Chittenden  Drum  Dam.     Eng.  Rec.     Vol.  40,  p.  356.     Sept.  16,  1899. 

23.  Claise,  M.     The  Resistance  of  Dam  Framing.     Ann  des  Fonts  et  Chaus- 

sees.     4  Trimestre,  1899. 

24.  A  New  Automatic  Movable  Dam.     Eng.  Rec.     Vol.  45,  p.  222.     March  8, 

1902. 

25.  Reconstruction  of  the  Lake  Winnibigoshish   Dam.     Eng.   Rec.     Vol.   46, 

p.  250.     Sept.  13,  1902. 

26.  Hilgard,    K.    E.     Roller    Dams.     Schweizerische    Bauzeitung.     Bd.    43    s. 

65  u.  86.     Feb.  6-13,  1904. 

27.  Koechlin,  Rene.     Large  Rolling  Dams.     Genie  Civil,  Feb.  27,  1904. 

28.  Guarini,    Emile.     Rolling   Dams   at    Schweinfurt,    Bavaria.     Eng.    News, 

vol.  53,  p.  57.     Jan.  19,  1905. 

29.  Walker,   Gilbert   S.     Pile  Foundations   for   Movable   Dam   at   McMechen, 

W.  Va.     Eng.  News,  vol.  54,  p.  100.     July  27,  1905. 

30.  Movable  Dam  and  Lock  -of  The  Rice  Irrigation  and  Improvement  Assoc., 

Mermentau  River,  La.    Eng.  News,  vol.  54,  p.  321.    Sept.  28,  1905. 

31.  Movable  Crest  Dams  at  the  Water  Power  Development  of  the  Chicago 

Drainage  Canal.     Eng.  Rec.     Vol.  56,  p.  194. 

32.  Johnston,  C.  T.     Masonry  and  Steel  Head  Gates  of  the  Grand  Valley  Ir- 

rigation Canal.     Engineering  News,  Vol.  50,  p.  141. 

33.  Hanna,  F.  W.     Electrically  Operated  Gates  for  the  Roosevelt  Dam.     Eng. 

News,  vol.  57,  p.  586. 

34.  Hanna,  F.  W.  Hydraulic  Gates  for  Drainage  Tunn«l,  Kern  River  Plant. 

Eng.  News,  vol.  51,  p.  326. 

35.  Leighton,   M.    O.     High   Pressure    Sluice   Gates.     Jour.   West.    Soc.   Eng. 

Vol.  II,  p.  381. 

36.  Gillette,  H.  P.     The  Rudder  Boom.     Eng.  News,  Vol.  47,  p.  473. 

FISHWAYS. 

1.  Gerhardt,  Paul.     Fischwege  and  Fischteiche.     Verlag  Von  Wilhelm  En- 

gelmann.     Leipzig,  1904. 

2.  Leslie,  Alexander.     Salmon  Ladders  in  Scotland.    Institute  of  C.  E.    Vol. 

89,  p.  304. 


CHAPTER  XXVI. 
PONDAGE  AND  STORAGE. 

331.  Effect  of  Pondage  on  Power. — The  terms  "Pondage"  and 
"Storage"  are  quite  similar  in  meaning,  both  having  reference  to 
the  impounding  of  water  for  future  use.  The  term  pondage  us- 
ually refers  to  the  smaller  ponds  which  permit  of  the  impounding 
of  the  night  flow  for  use  during  the  working  hours  of  day.  Stor- 
age, on  the  other  hand,  is  usually  applied  to  the  larger  impounding 
reservoirs  that  enable  a  sufficient  quantity  of  water  to  be  stored 
to  carry  the  plant,  to  some  extent  at  least,  through  the  dry  season 
of  the  year.  Between  these  limits  every  variation  in  capacity  is 
of  course  possible. 

In  Chapter  IV,  Section  54,  the  effect  of  pondage  on  the  power 
of  a  stream  is  briefly  outlined  and  illustrated  by  hydrographs 
shown  in  Figs.  41  and  42.  The  pondage  illustrated  by  these  dia- 
grams is  sufficient  to  store  the  entire  flow  of  the  river  during  the 
parts  of  the  day  when  the  power  is  not  in  use  and  reserve  it  for 
those  hours  of  the  day  when  the  power  is  needed.  Such  a  condi- 
tion can  frequently  be  realized  for  the  low  flows  during  the  dry 
seasons,  but  the  capacity  is  seldom  sufficient  to  store  the  larger 
flows,  and  if  sufficient  should  be  investigated  in  a  different  manner 
to  be  discussed  later.  These  hydrographs  (Figs.  41  and  42) 
should  therefore  be  examined  with  these  points  in  view. 

In  many  water  power  installations  practically  no  pondage  is  pos- 
sible and  the  power  of  the  stream  must  be  utilized  as  it  flows  or 
otherwise  it  will  be  wasted.  On  continuous  service,  such  as  is 
sometimes  required  by  cotton  factories,  paper  mills,  and  electro- 
chemical works  that  run  twenty-four  hours  per  day,  pondage  is  not 
so  essential.  With  most  power  loads,  such  as  are  shown  by  the 
various  load  curves  in  Chapter  XVII,  the  night  load  is  small  and 
the  pondage  of  the  night  flow  will  frequently  permit  of  more  than 
doubling  the  power  that  can  be  otherwise  utilized. 

312.  Effect  of  Limited  Pondage  on  the  Power  Curve. — Fre- 
quently limited  pondage  only  is  possible  and  its  influence  on  the 
possible  power  that  can  be  generated  must  be  carefully  investigated. 


Effects  of  Limited  Pondage  on  the  Power  Curve.        625 

If  power  is  to  be  used  for  a  limited  number  of  hours  each  day,  the 
rate  at  which  power  can  be  used  for  this  time  without  pondage  will 
be  the  same  as  for  thet  continuous  power  of  the  stream. 

Such  proportions  of  the  otherwise  unutilized  flow  of  the  stream 
as  can  be  impounded  during  periods  of  light  load  can  be  added  to 
the  daily  output.  Thus,  if  power  is  used  for  12  hours  per  day,  and 
the  night  flow  can  be  impounded  and  utilized  during  the  day,  the 
day  power  will  be  increased  to  double  what  it  otherwise  would  be. 

If  power  is  used  for  only  ten  hours  per  day,  with  perfect  pondage 
the  day  power  will  be  increased  to  2.4  of  what  it  would  otherwise 
be. 

In  twelve  hours  there  are  43,200  seconds,  and  in  each  acre  there 
are  43,560  square  feet,  it  can  therefore  readily  be  remembered  that 
for  twelve  hour  pondage  there  must  be  practically  as  many  acres 
one  foot  deep  (or  acre  feet)  in  the  pond  as  there  are  cubic  feet  per 
second  to  be  impounded.  For  ten  hour  use  and  fourteen  hour 
storage,  the  pond  area  must  be  increased  by  one  sixth  above  the 
capacity  needed  for  twelve  hour  service.  For  example:  In  order 
to  utilize  the  full  flow  of  the  Wisconsin  River  at  Kilbourn  in  twelve 
hours,  (see  Fig.  39)  on  the  day  of  lowest  flow  (in  August,  1904),  a 
pondage  of  3,000  acre  feet  would  have  been  necessary,  and,  to  util- 
ize this  full  flow  in  ten  working  hours,  would  have  required  a  pon- 
dage of  about  3,500  acre  feet. 

Where  the  depth  of  pondage  is  considerable  the  effect  of  the 
variation  in  head  on  the  power  should  receive  careful  consideration. 

313.  Power  Hydrograph  at  Sterling,  Illinois. — In  1903  the  writer 
was  retained  to  investigate  the  probable  effect,  on  the  water  power 
at  Sterling,  Illinois,  of  the  proposed  diversion  of  water  for  feeding 
the  Illinois  and  Mississippi  or  "Hennepen"  Canal. 

The  pondage  formerly  available  at  Sterling,  by  using  eighteen 
inch  flash  boards  on  the  dam,  was  about  42,000,000  cubic  feet  (al- 
most 1,000  acre  feet). 

The  diversion  dam  at  Sterling  has  been  constructed  about  one 
mile  above  the  dam  of  the  Sterling  Hydraulic  Company  and  has 
limited  the  available  pondage  to  an  area  of  about  5,000,000  sq.  ft., 
and  a  pondage  of  about  7,000,000  cubic  feet.  This  change  has  there- 
fore caused  a  loss  of  pondage  of  about  35,000,000  cubic  feet,  which 
represents  the  night  storage  (i.  e.,  the  storage  during  the  fourteen 
hours  of  night),  of  700  cubic  feet  per  second,  which  represents  980 
hydraulic  horse  power  for  the  ten  hours  of  day.  That  is  to  say, — 
the  loss  of  35,000,000  cubic  feet  of  storage  capacity  caused  by  the 


626 


Pondage  and  Storage. 


QQ 


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s 


Effects  of  Pondage  on.  Other  Power.  627 

construction  of  the  U.  S.  Government  dam  near  the  mouth  of  the 
Illinois  and  Mississippi  Canal,  has  lost  to  the  Sterling  Hydraulic 
Company  about  980  hydraulic  horse  power  during  such  periods  as 
the  flow  of  the  river  is  more  than  840  cubic  feet  per  second,  and 
less  than  the  capacity  of  the  wheels  installed  (i.  e.,  4,450  cubic  feet 
per  second). 

Fig.  388  gives  a  graphical  illustration  of  the  effects  of  storage  on 
the  normal  water  power^at  Sterling  and  the  loss  resulting  from  the 
loss  of  storage.  The  lower  flow  line  is  the  line  of  the  normal  hy- 
draulic horse  power  of  the  Rock  River  for  continuous  (twenty-four 
hour)  service.  It  also  shows  the  total  power  available  for  ten-hour 
service  without  pondage.  The  flow  line  just  above  the  line  of 
normal  power,  and  parallel  thereto,  shows  the  additional  ten-hour 
power  available  from  a  pondage  of  7,000,000  cubic  feet.  The  upper 
flow  line  shows  the  ten-hour  power  made  available  by  the  storage 
of  42,000,000  cubic  feet.  The  hatched  area  between  lines  two  and 
three  represents  therefore  the  loss  in  ten-hour  power  which  has 
been  caused  by  the  loss  in  storage  of  36,000,000  cubic  feet. 

From  this  diagram  it  will  be  noted  that  when  the  flow  of  the 
river  is  sufficient  to  supply  the  wheels,  no  loss  would  be  occasioned 
by  the  loss  in  pondage,  and,  as  the  flow  approaches  this  point,  the 
actual  loss  decreases.  It  should  also  be  noted  that  when  the  flow 
of  the  river  is  less  than  840  cubic  feet  per  second  (above  the 
amount  diverted  by  the  canal)  the  total  storage  of  42,000,000  cubic 
feet  is  more  than  necessary  to  store  the  night  flow,  hence  the  loss 
at  such  times  caused  by  loss  of  pondage  also  decreases. 

The  approximate  total  loss  of  power  for  the  year  caused  by  the 
loss  of  35,000,000  cubic  feet  of  storage,  as  measured  from  this 
diagram,  is  980  hydraulic  horse  power  for,  approximately,  250  ten- 
hour  days. 

314.  Effect  of  Pondage  on  Other  Power. — The  pondage  of  water 
during  the  night  naturally  interferes  with  the  normal  flow  of  the 
stream  and  alters  the  regimen  of  the  river  at  points  below  the  point 
of  pondage.  The  effect  of  such  interference  on  other  power,  and 
the  effect  of  other  ponds  on  the  plant  contemplated,  should  be 
carefully  considered. 

Fig.  389  is  a  hydrograph  of  the  Fox  River  taken  from  observa- 
tion by  the  Government  Engineers  at  Rapid  Croche,  Wisconsin. 
Above  this  point  are  a  number  of  water  power  dams.  Many  of  the 
plants  run  twenty-four  daily,  but  close  down  on  Sundays.  The  ef- 


Pondage  and  Storage. 


m  h>  to  in  ^t  n 

ON033S       U3d       133J       DI8R3       Nl       33UVH3SIQ 


Effect  of  Limited  Storage. 


629 


feet  of  the  Sunday  shut-down  on  the  stream  flow  is  well  shown  in 
the  hydrograph  and  is  evident  even  during  flood  periods. 

315.  Effect  of  Limited  Storage. — When  the  pondage  'available  is 
more  than  sufficient  to  carry  the  night  flow  of  the  low  water  period 
over  for  day  use,  it  becomes  possible  to  equalize,  to  a  greater  or  less 
extent,  the  variation  in  daily  flow  and  to  utilize  excess  flow  to  in- 
crease deficient  flows,  thus  raising  the  quantity  of  available  contin- 
uous power.  The  extent  of  this  equalization  depends  on  the  quan- 
tity of  storage  and  can  readily  be  investigated  graphically. 

Fig.  390  shows  the  estimated  daily  flow  of  the  Wisconsin  River  at 
Kilbourn  for  July,  August,  and  September,  the  low  water  period) 
1904.  From  this  hydrograph  it  will  be  seen  that  the  lowest  flow  is 
3,000  cubic  feet  per  second.  From  Sec.  312  it  is  seen  that  in  order 
to  utilize  the  night  flow  during  the  twelve  hours  of  day,  a  pondage 
of  3,000  acre  feet  must  be  available.  With  such  a  pondage  the 


16,000 

14,000 

12,000 

10,000 

8,000 

6,000 

4.0OO 

2,000 

O 


JULY  AUGUST  SEPTEMBER 

Fig.  390. — Low  Water  Flow  at  Kilbourn  and  Storage  Capacity  Necessary  to 
Augment  it  to  Various  Amounts. 


night  flow  can  ordinarily  be  distributed  so  as  to  be  available  either 
for  twelve  hour  constant  power  or  to  furnish  power  for  any  equiv- 
alent load  curve. 

In  Fig.  390  the  horizontal  spaces  each  represent  a  flow  of  1,000 
cubic  feet  per  second,  and  the  vertical  spaces,  one  day.  The  area 
of  each  space  therefore,  represents  86,400,000  cubic  feet,  or  ap- 
proximately 2,000  acre-feet. 

To  increase  the  low  water  flow  of  the  river  to  4,000  second  feet 
will  require  a  storage  capacity  equivalent  to  that  represented  by  ap- 
proximately three  spaces,  or  a  storage  of  6,000  acre-feet  in  addition 
to  the  pondage,  or  a  total  storage  of  about  9,000  acre  feet.  To  in- 


630  Pondage  and  Storage. 

crease  the  flow  to  5,000  second  feet,  a  total  storage  of  28,000  acre- 
feet  in  addition  to  the  pondage  would  be  required;  and  a  flow  of 
6,000  second  feet,  will  require  a  storage  of  90,000  acre  feet  in  addi- 
tion to  the  pondage.  In  this  latter  case  the  conditions  to  Sept.  6th 
must  be  considered,  for  the  increased  flow  from  August  I2th  to  I7th 
is  not  sufficient  to  fill  the  reservoir,  although  it  will  reduce  the 
capacity  required,  as  will  also  the  increased  flow  of  August  2oth. 

The  reservoir  capacity  represented  by  90,000  acre  feet  is  shown 
on  the  diagram  both  by  the  curved  hatched  area  above  the  flow- 
line  and  by  the  rectangular  shaded  area  as  well. 

If  the  reservoir  capacity  is  known,  and  its  equivalent  repre- 
sented on  the  drawing,  its  effect  on  the  hydrograph  can  readily  be 
determined  by  trial.  (See  also  Fig.  393.) 

316.  Effect  of  Large  Storage. — When  large  storage  is  available, 
the  daily  flow  of  a  stream  can  be  equalized  and  its  variations  there- 
fore becomes  less  important.  In  such  cases  the  power  of  a  plant 
depends  on  the  average  weekly  or  monthly  flow  of  the  stream  and 
the  possible  storage  capacity. 

S.  B.  Hill,  C.  E.,  has  suggested  a  method  of  discussing  the  effect 
of  storage  on  the  flow  and  power  of  a  stream  which  is  well  illus- 
trated by  Figs.  391  and  392.  These  hydrographs  were  prepared  by 
the  writer  to  illustrate  a  report  on  the  probable  power  of  a  pro- 
posed hydraulic  development  in  the  South.  Figs.  391  represent 
the  mean  monthly  flow  of  the  river  in  question  for  the  years  1893 
to  1906  inclusive.  In  this  case  the  scale  above  the  zero  line  shofws 
both  the  mean  monthly  flow  of  the  stream  in  cubic  feet  per  sec- 
ond and  the  mean  monthly  power  of  the  stream  in  horse  power 
hours  per  day  with  the  head  available.  The  available  storage  is 
here  51,000  acre  feet  or  2,221,560,000  cubic  feet.  This  storage  is 
equivalent  to  a  flow  of  857  second  feet  for  thirty  days,  or  a  stor- 
age of  energy,  with  the  available  head,  of  about  5,000,000  horse 
power  hours. 

The  maximum  daily  continuous  power  (see  A-A,  Fig.  391)  is 
determined  by  the  effect  of  the  driest  year  (viz.  1904)  on  the  stor- 
age. The  effect  of  the  dry  periods  on  the  storage  is  shown  by  the 
incisions  into  the  lower  or  storage  line  of  trie  diagram.  In  the 
year  1904  the  reservoir  capacity  would  have  been  just  exhausted 
in  order  to  maintain  the  power  during  the  low  flows  of  September, 
October  and  November  of  that  year.  The  amount  of  available  con- 
tinuous energy  (i.  e.  the  position  of  the  line  A-A)  is  determined 


Effect  of  Auxiliary  Power.  631 

by  equalizing  the  deficiency  in  flow  during  the  dry  months  with 
the  total  reservoir  capacity. 

It  is  important  in  the  study  of  storage  to  see  that  in  the  inter- 
vening periods  of  excessive  flow,  such  flows  are  sufficient  to 
supply  the  deficiency  occasioned  by  previous  demands  on  the  res- 
ervoir, otherwise  the  effect  of  one  dry  period  must  be  considered 
in  its  relation  to  subsequent  periods  in  determining  the  available 
continuous  power  (see  Fig.  391,  1897  and  1898). 

The  daily  flow  of  this  river  for  the  year  1904  is  shown  by  the 
hydrograph,  Fig.  393,  from  which  it  will  be  seen  that  with  pondage, 
but  without  storage,  the  available  power  of  this  stream  would  be 
limited  to  a  minimum  of  27,000  horse  power  hours  per  day. 

317.  Effect  of  Auxiliary  Power. — In  order  to  maintain  a  con- 
tinuous power  greater  than  that  due  to  the  minimum  flow  of  the 
stream  plus  the  pondage,  some  source  of  auxiliary  power  must  be 
available.  If  it  is  desired  to  increase  the  power  of  the  stream  rep- 
resented in  Fig.  391  by  50,000  horse  power  hours  per  day,  making 
the  total  horse  power  hours  delivered  163,400  (represented  by  line 
B-B,  Fig.  392),  auxiliary  power,  as  represented  by  the  shaded  areas 
on  this  diagram,  would  be  needed.  As  at  all  other  times  water 
power  would  be  available,  the  addition  of  steam  auxiliary  power 
would  apparently  be  warranted.  The  size  of  the  plant  needed  to 
furnish  such  excess  power  would  depend  on  the  method  of  power 
utilization.  It  is  evident  that  during  the  dry  periods  in  1899,  1904 
and  1905,  if  the  water  power  was  first  used  to  its  maximum,  and  the 
storage  exhausted,  an  auxiliary  plant  would  be  needed  of  a  capacity 
almost  equal  to  the  maximum  demand  on  the  plant,  and  that  a 
plant  of  less  capacity  could  be  utilized  satisfactorily  only  by  operat- 
ing it  to  a  considerable  capacity  whenever  a  considerable  draft  be- 
gan to  be  made  on  the  storage.  As  the  extent  of  the  drought,  or 
deficiency  of  water,  could  not  be  anticipated  such  a  use  of  the 
auxiliary  plant  would  require  a  greater  expenditure  of  auxiliary 
horse  power  hours  than  is  represented  by  the  shaded  areas  in  Fig. 

392. 

An  investigation  of  the  capacity  and  amount  of  auxiliary  power 
needed,  without  pondage  or  storage,  to  maintain  a  given  continu- 
ous power,  can  be  readily  made  from  the  hydrograph  of  daily  flow 
as  shown  by  Figs.  394  and  395  which  represent  such  a  study  of  the 
Rock  River  at  Sterling,  Illinois,  before  the  diversion  of  water  for 
use  in  the  Illinois  and  Mississippi  canal,  and  the  probable  addi- 


Fig.  391. — Mean  Monthly  Flow  of  a  Southern  Rive 


Fig.   392. — Amount   of  Auxiliary   Power  Nec< 


I3SOOQ 
08000 
81000 
54000 
27000 
0 


U) 


id  Effect  Thereon  of  a  Given  Reservoir  Capacity 


2000 
135000 
108000 
81000 
54000 
27000 
0 


ry  to   Increase   Output  by  50,000  H.  P.  H. 


634 


Pondage  and  Storage. 


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Calculations  for  Storage. 


635 


tional  auxiliary  power  required  to  maintain  the  same  power  after 
such  diversion. 

318.  Effect  of  Maximum  Storage. — As  the  head  increases  the 
quantity  of  water  needed  to  develop  a  given  amount  of  power  de- 
creases, and  storage  becomes  of  much  greater  relative  value.  The 
storage  of  comparatively  small  quantities  of  water  also  becomes 
a  more  simple  matter,  but  conditions  which  need  little  consideration 
with  larger  flows  and  lower  heads,  then  become  more  important-  In 
such  cases,  relatively,  large  reservoir  capacity  sometimes  becomes 


Fig.    394. — Hydrograph    Showing    Auxiliary    Power    Necessary    to    Maintain 
4450  Ten-hour  Horse  Power  at  Sterling,  111. 


Fig.   395. — Hydrograph   Showing  Auxiliary  Power   Needed  to   Maintain  Ca- 
pacity of  Wheels  and  Probable  Increase  Due  to  Diversion  of  Water 
for  Illinois  and  Mississippi  Canal. 

possible  and  only  the  questions  of  desirability  and  cost  limit  the 
extent  to  which  such  storage  may  be  carried. 

319.  Calculations  for  Storage.— Rippl  has  outlined  a  method  of 
coimputing  storage  which  may  occasionally  be  used  to  advantage 
under  high  head  conditions,  when-  it  is  desired  to  utilize  the  average 
flow  of  a  series  of  dry  months  or  years  by  extensive  storage.  This 
method  consists  in  graphically  representing  the  net  yield  of  the 


636 


Pondage  and  Storage. 


stream  during  the  period  of  low  flow  and  from  the  curve  of  the  net 
flow  estimating  the  quantity  of  storage  necssary  for  its  full  utiliza- 
tion. 

The  method  suggested  may  be  illustrated  as  follows : 

From  a  study  of  the  hydrographic  conditions  on  the  water  shed 

for  a  considerable  term  of  year,  the  period  of  extreme  low  flow 

is  selected.     For  this  period  the  observed  or  estimated  flow  of  the 

stream  for  each  month  is  reduced  by  the  loss  due  to  evaporation, 

800,000 


700,000 


SCALE    OF    MONTHS 

Fig.  396.— Diagram  Illustrating  Rippl  Method  of  Calculating  Storage. 

seepage,  etc.  The  remainder  represents  the  net  quantity  of  water 
available  for  power  purposes,  The  summation  of  these  monthly 
balances,  added  one  to  the  other  consecutively  can  be  platted  in  a 
curve  in  which  the  abscissa  of  each  point  represents  the  total  time 
from  the  beginning  of  the  period ;  and  the  ordinate,  the  total  quan- 
tity of  water  available  during  the  same  interval.  The  scale  may 
represent  inches  on  the  drainage  areas,  cubic  feet,  acre  feet,  or 
such  other  unit  as  may  be  desired.  Such  a  curve  is  represented  in 
Fig.  396  by  the  irregular  curve  A-B-OD-E-F.  The  inclination  of 
Lhe  curve  at  any  point  indicates  the  rate  of  the  net  flow  at  that  par- 


Calculations  for  Storage.  637 

ticular  time.  When  the  curve  is  parallel  to  the  horizontal  axis,  the 
flow  at  that  time  will  just  balance  the  losses  caused  by  evapora- 
tion, seepage,  etc.  A  negative  inclination  of  the  supply  line  shows 
that  a  loss  from  the  reservoir  is  taking  place. 

In  a  similar  manner  the  curve  of  consumption  can  be  platted. 
For  most  purposes  this  can  be  considered  a  straight  line  as  the  var- 
iation in  the  use  of  power  from  season  to  season  is  a  refinement  not 
usually  warranted,  unless  the  uses  to  which  the  power  is  to  be  put 
at  various  times  of  the  year  are  well  established.  In  Fig.  396  a 
series  of  straight  lines  of  consumption  are  drawn,  representing  the 
use  of  water  at  rates  of  100  to  600  acre  feet  per  day.  These  rates 
correspond  essentially  to  rates  of  from  50  to  300  cubic  feet  per  sec- 
ond. 

The  ordinate  between  the  supply  and  any  demand  line  represents 
the  total  surplus  from  the  beginning  of  the  period  considered,  and 
when  inclination  of  the  supply  line  is  less  than  that  of  the  demand 
line,  the  yield  of  the  drainage  area  is  less  than  the  demand  and  a 
reservoir  is  necessary. 

The  deficiency  occurring  during  dry  periods  is  found  by  drawing 
lines  parallel  to  the  demand  line,  or  lines,  and  tangent  to  the  curve 
at  the  various  summits  of  the  supply  curve,  as  at  B. 

The  maximum  deficiency  in  the  supply,  and  the  necessary  capac- 
ity of  the  reservoir  to  maintain  the  demand  during  the  period,  is 
shown  by  the  maximum  ordinate  drawn  from  the  tangent  to  the 
curve  itself.  The  period  during  which  the  reservoir  would  be 
drawn  below  the  high  water  line  is  represented  by  the  horizontal 
distance  between  the  tangent  point  and  the  first  point  of  inter- 
section of  the  curve.  If  the  tangent  from  any  summit  parallel  to 
any  demand  line  fails  to  intersect  the  cu,rve,  it  indicates  that,  during 
that  period,  the  supply  is  inadequate  for  the  demand.  To  insure  a 
full  reservoir  it  is  necessary  that  a  parallel  tangent  drawn  backward 
from  the  low  points  on  the  supply  curve  shall  intersect  the  curve  at 
some  point  below.  For  example:  The  line  B-7,  representing  a  daily 
consumption  of  700  acre  feet,  does  not  again  intersect  the  curve 
and  is  therefore  beyond  the  capacity  of  the  stream.  The  line  B-6 
intersects  the  curve  at  E  and  is  the  limit  of  the  stream  capacity. 
Such  a  consumption  will  be  provided  by  a  storage  of  about  150,000 
acre  feet  as  represented  by  the  length  of  the  line  6-D,  and  such  a 
reservoir  will  be  below  the  flow  line  for  about  twenty-two  months 
during  the  dry  period  illustrated  in  this  diagram.  That  this  reser- 
voir will  fill  is  shown  by  the  intersection  of  the  lower  tangent  D-A 


63S 


Pondage  and  Storage. 


with  the  curve  near  A.  The  conditions  necessary  to  maintain 
capacities  of  500,  400  and  300  second  feet  are  shown  respectively  by 
the  tangents  B-5,  B-4  and  B-3,  and  the  verticals  5-D,  4-C  and  3-C. 
If  the  amount  of  storage  is  known,  and  it  is  desired  to  ascertain 
the  maximum  demand,  that  can  be  satisfied  by  such  fixed  capacity, 


ORYEST  FIVE  CONSEC 


1MT        1M0        IBM 


Fig.  397. — Diagram  Showing  Annual  Run-off  from  Tohickon  Creek. 

the  rate  is  determined  by  drawing  various  tangent  lines  from  the 
summits,  having  the  maximum  ordinates  equal  to  the  fixed  storage. 
320.  Method  of  Storage  Calculations. — The  results  of  calcula- 
tions, as  outlined  in  Sec.  319  for  various  conditions  of  storage  on 
Tohickon  Creek,  are  shown  in  Table  XXXIX  and  Fig.  398.  To- 
hickon Creek  is  one  of  the  possible  sources  of  water  supply  which 
has  been  investigated  by  the  City  of  Philadelphia  for  a  considerable 
period.  The  observed  monthly  rainfalls  and  stream  flows  from  the 
drainage  area  of  this  stream  (in  inches  on  the  drainage  area)  are 
given  in  Tables  XL  and  XLI.  The  five  year  period  of  minimum 
flow  is  found  by  inspection  to  run  from  December,  1893,  to  Novem- 
ber, 1898,  as  shown  by  Fig.  397.  The  approximate  evaporation  dur- 
ing the  period  is  taken  from  Appendix  F. 

The  calculations  of  the  mass  curves  are  based  on  the  extreme 
variations  in  reservoir  area  of  o  to  100  per  cent ;  that  is,  on  the  as- 


Method  of  Storage  Calculations. 


639 


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TABLE  XL. 

Toliickon  Creek— Monthly  Rainfall  in  Inches. 


Year. 

S 

h-  ; 

& 
O> 
M 

c 

CS 

S 

s_' 

CU 
< 

>* 

o3 
*^ 

0; 

d 

H^ 

1-5 

hb 

< 

"a. 

£ 

^ 

8 

1 

d 

1 

£.&§ 

8  £  tj 
pHpii-- 

1886  

4.15 
4.24 
5.31 
4.23 
2.82 
6.14 
5  49 

6.01 
5.47 
4.34 
2.37 
4.73 
4.58 
1.23 
5.88 
3.96 
.96 
7.90 
3.10 
3.38 
4.75 
4.08 

4.76 
3.07 
5.23 
3.67 
6.77 
4.79 
4.13 
2.46 
1.65 
3.11 
5.44 
2.46 
2.84 
6.60 
4.04 

3.42 
2.42 
4.08 
4.90 
2.48 
1.97 
1.95 
4.96 
2.91 
5.50 
1.48 
3.20 
3.73 
2.19 
3.33 

7.14 
2.59 
3.03 
5.41 
6.30 
2.83 
5.55 
4.98 
13.50 
2.99 
3.18 
8.90 
7.62 

9   93 

174 

4.53 
5.77 
1.69 
6.94 
3.93 
3.38 
3.20 
4.05 
2.63 
4.49 
4.07 
5.10 
.76 
2.74 
3.95 

5.47 
8.13 
3.20 
12.33 
5.81 
7.49 
4.27 
2.10 
2.28 
3.53 
8.06 
8.47 
4.00 
3.29 
5.42 

1.08 
5.30 
8.07 
4.63 
5.75 
8.90 
3.76 
8.67 
2.03 
4.43 
1.63 
4.75 
6.05 
5.05 
4.93 

1.30 
3.36 
8.32 
7.92 
2.98 
1.37 
2.91 
3.20 
9.44 
.68 
5.83 
1.92 
2.03 
6.70 
4.16 

2.59 
1.93 
4.06 
4.57 
6.31 
3.81 
.64 
3.72 
5.18 
3.86 
2.67 
1.83 
5.21 
1.39 
3.71 

5.16 
1.42 
3.66 
8.86 
1.07 
1.97 
7.10 
4.37 
3.01 
2.11 
4.08 
5.02 
3.56 
2.55 
3.33 

3.83 
6.53 
4.35 
1.99 
2.75 
5.09 
1.57 
3.17 
4.60 
2.57 
.94 
4.64 
3.49 
2.34 
3:78 

49.45 
50.22 
55.34 
68.04 
51.60 
52.32 
41.80 
50.52 
53.01 
38.24 
46.46 
50.59 
46.92 
43.51 
49.11 

1887   

1888  
1889  

1890  

1891 

1892 

1893 

2.96 
1.82 
4.19 
1.18 
2.20 
4.19 
3.68 
3.64 

1894  

1895 

1896  

1897 

1898 

1899  
Average  

TABLE  XLI. 
Tohickon  Creek — Monthly  Discharge  in  Inches  on  Drainage  Area. 


Year. 

oS 

1-5 

J3 
<D 
(* 

•  il 
oi 
^ 

s_' 
PH 
< 

!>» 

OS 

£ 

6 

G 

>-5 

>> 

»-5 

hi> 

< 

<5« 

& 

•4^ 

§ 

6 
to 

cj 

& 

t-& 

£.2* 
^P-g 

1886  
1887  
1888  

1889 

4.36 
5.04 
6.38 
4.38 
2.06 
6.15 
6.53 
2.22 
.80 
3.95 
.54 
1.81 
3.70 
4  7?, 

9.19 
5.25 
6.72 
1.51 
3.78 
5.68 
1.19 
6.64 
3.80 
1.70 
i.59 
2.92 
4.05 
5.56 
4.25 

4.28 
3.84 
6.27 
3  86 
6.37 
5.03 
4.87 
4.54 
3.09 
5.37 
5.48 
2.19 
1.83 
8.99 
4.70 

4.75 
1.02 

4.28 
2.88 
1.79 
1.58 
.84 
3.22 
2.28 
4.65 
.73 
1.55 
2.50 
1.57 
2.50 

3.43 
.93 
.52 
1.70 
3.09 
.28 
2.05 
3.79 
8.58 
.66 
.30 
4.63 
5.04 
.25 
2.08 

1.41 
1.21 
.15 
2.29 
.75 
.17 
.70 
.45 
.53 
.27 
.18 
1.71 
.19 
.07 
.76 

.77 
1.63 
.06 
6.41 
.87 
.90 
.51 
.10 
.19 
.80 
2.54 
2.68 
.07 
.08 
1.15 

.09 
1.96 
1.77 
3.75 
.92 
8.92 
.30 
1.56 
.12 
37 
.19 
.73 
.74 
1.02 
1.19 

.03 
.40 
5.50 
3.40 
1.22 
.94 
.19 
.83 
3.37 
.03 
1.12 
.12 
.08 
2.26 
1.36 

.05 
.25 
1.54 
2.33 
3.54 
.46 
.09 
.60 
2.10 
.09 
1.06 
.07 
.60 
.19 
1.20 

1.91 
.25 
3.11 
7.97 
.69 
.63 
3.19 
2.62 
2.67 
.13 
2.34 
1.79 
4.50 
1.02 
1.89 

2.38 
3.20 
3.47 
1.92 
1:51 
4.27 
1.67 
3.10 
3.57 
.67 
.80 
4.08 
4.23 
1.28 
2  89 

32.65 
24.98 
39.77 
42.40 
26.59 
30.01 
22.13 
29.67 
31.10 
18.69 
19.87 
24.28 
27.53 
27.01 
27.58 

1890  
1891  

1892 

1893 

1894. 

1895  .,.. 
1896  
1897  
1898  

1899  

Average  

3.59 

sumption  that  the  reservoir  may  occupy  from  nothing  to  the  en- 
tire drainage  area. 

The  conditions  on  the  reservoir  area  are  those  due  to  the  equal- 
ization  of  the   rainfall  with   the   evaporation,   seepage  and   other 


644  Pondage  and  Storage. 

losses.  The  conditions  on  the  balance  of  the  water  shed  are  given 
by  the  run-off  and  its  summation. 

Table  XXXIX  shows  these  calculations  in  detail  and  the  mass 
curves  drawn  from  columns  6,  10,  14,  18  and  19  are  platted  in  Fig. 
398.  The  maximum  continuous  power  which  could  be  maintained 
throughout  this  period  without  storage  is  shown  by  the  lowest 
slopes  of  the  zero  per  cent,  mass  curve.  The  possible  maximum  de- 
velopment of  the  stream  with  various  percentages  of  reservoir  area 
can  be  determined  by  an  analysis  of  the  lower  curves  similar  to  that 
described  in  Sec.  319. 

321.  Analytical  Methods. — Graphical  methods  o;f  computation 
have  been  heretofore  suggested  as  a  means  of  investigating  pondage 
and  storage  conditions.  Such  methods  are  believed  to  be  advanta- 
geous in  most  cases  on  account  of  presenting  visible  evidence  which 
can  usually  be  more  clearly  understood  than  an  abstract  analysis. 

Analytical  methods  for  the  consideration  of  these  questions  are 
usually  obvious  after  the  graphical  methods  discussed  are  under- 
stood, and  such  methods  should  usually  be  used  to  check  up  the 
graphical  deductions.  Such  methods  may  be  illustrated  by  the  fol- 
lowing analysis  of  the  effect  of  low  water  conditions  on- a  proposed 
water  power  on  a  Western  river  on  which  the  writer  recently  fur- 
nished a  report. 

In  this  case  daily  guage  readings  were  available  for  about  ten 
years,  and  the  rainfall  records  were  available  for  a  considerably 
longer  period. 

From  these  records  it  appeared  that  the  year  1905  was  the  driest 
year  on  record,  and  that  the  power  available  during  the  low  water 
period  of  that  year  would  have  been  equalled  at  least  at  all  times 
during  every  year  in  the  past  twenty  years,  and  with  a  probable  like 
result  in  the  future. 

At  the  proposed  plant  each  cubic  foot  per  second,  flowing  during 
a  day  of  twenty-four  hours,  will,  at  80  per  cent,  efficiency,  produce 
3.63  continuous  horse  power.  In  order  to  develop  8,000  twenty-four 
hour  horse  power,  it  would  be  necessary,  therefore,  to  have  avail- 
able a  continuous  flow  of  2,200  second  feet,  while  the  minimum  flow 
in  1905  was  only  1240  second  feet.  An  examination  of  the  gaug- 
ings  shows  that  during  the  dry  period  of  1905  the  water  was  defi- 
ient  in  quantity  for  sixty-eight  days.  The  average  flow  for  this  pe- 
riod was  1,700  second  feet,  causing  an  average  deficiency  of  500 
second  feet.  To  impound  sufficient  water  to  maintain  2,200  second 
feet  would  require,  therefore,  a  storage  capacity  of  about  1,000  acre 


Literature.  645 

feet  for  each  day  of  the  dry  period,  or  a  total  reservoir  capacity  of 
about  68,000  acre  feet.  Above  the  proposed  dam  site  is  a  lake  hav- 
ing an  area  of  about  60  square  miles  or  38,400  acres.  By  raising  the 
level  of  this  lake  two  feet  a  storage  of  76,800  acre  feet  would  be  at- 
tainable which,  with  careful  manipulation  would  be  sufficient  to 
maintain  the  desired  power. 

If  no  storage  were  possible,  and  auxiliary  power  was  to  be  es- 
tablished, the  maximum  capacity  of  the  auxiliary  plant  would  be 
determined  by  the  day  of  lowest  flow.  During  this  day  there  was  a 
deficiency  of  960  second  feet,  equivalent  to  about  3,500  horse  power 
The  average  deficiency  for  the  period  was  500  second  feet,  rep- 
resenting a  necessary  average  of  auxiliary  power  of  1815  horse 
power,  or  43,560  horse  power  hours  per  day.  The  total  auxiliary 
power  for  this  period  (68  days)  would  therefore  be  about  3,000,000 
horse  power  hours. 

In  the  same  manner  the  total  amount  of  auxiliary  power  neces- 
sary during  each  year  could  be  estimated  and  the  interest  and  de- 
preciation on  the  cost  of  the  plant,  plus  the  average  annual  operating 
expenses  of  the  auxiliary  plant,  when  considered  in  connection  with 
similar  elements  of  the  water  power  installation,  would  furnish 
the  basis  for  an  estimate  of  the  first  cost  and  operating  expenses  of 
the  combined  plant  to  develop  the  required  power. 


LITERATURE. 

1.  Rippl,  W.     The  Capacity  of  Storage-Reservoirs  for  Water  Supply.     Insti- 

tute of  Civil  Engineers,  vol.  71,  p.  270. 

2.  Fitzgerald,   Desmond.     Report  on   Capacity   of   the   Sudbury  River   and 

Lake  Cochituate  Water  Sheds  in  Time  of  Drought.    New  Eng. 
Water  Works  Asso. 

3.  Fitzgerald,  Desmond.     Methods  Used  to  Determine  the  Best  Capacity  to 

Give  to  Basin  No.  5,  Boston  Water  Works.    Asso.  of  Eng.  Soc. 
Vol.  X,  p.  431. 

4.  Greenleaf,  J.  L.    A  Method  for  Determining  the  Supply  from  a  Given 

Water  Shed.     Eng.  News,  vol.  33,  p.  238. 

5.  Horton,  Theodore.     A  Form  of  Mass  Diagram  for  Studying  the  Yield  of 

Water  Sheds.     Eng.  Rec.     Vol.  36,  p.  185. 

6.  Turneaure    and    Russell.     Public    Water    Supplies.    Chapter    XV.     John 

Wiley  &  Sons. 

7.  Mead,  Daniel  W.     Report  on  the  Water  Power  of  the  Rock  River  at  Ster- 

ling and  Rock  Falls,  111.     1904. 


CHAPTER  XXVII. 

COST,  VALUE  AND  SALE  OF  POWER. 

322.  Financial  Considerations. — Every  engineer  who  is  called 
upon  to  advise  as  to  the  commercial  feasibility  of  a  proposed  water 
power  development  must  carefully  consider  all  financial  aspects  of 
the  project,  for  on  its  financial  feasibility  the  entire  commercial  suc- 
cess depends.  It  is  not  enough  that^the  power  be  constant  and  suffi- 
cient in  quantity,  that  the  plant  be  well  designed,  and  that  the  cost 
of  the  same  be  reasonable ;  but  there  must  also  be  a  market  in  which 
the  power  can  be  utilized  to  advantage  and  the  price  at  which  the 
power  can  be  sold  in  competition  with  all  other  sources  of  power 
must  be  sufficient  to  pay  all  expenses  involved  in  the  construction 
and  operation  of  the  plant  and  afford  a  fair  return  to  those  who  as- 
sume the  risk  of  the  undertaking. 

It  is  a  common  belief  that  any  water  power  development  must  be 
profitable.  Knowing  that  an  undeveloped  water  power  is  a  contin- 
ual waste  of  energy,  it  is  commonly  assumed  that  the  saving  of  this 
waste  is  bound  to  result  in  a  profit  to  those  who  acquire  the  prop- 
erty and  develop  the  power.  That  many  water  powrs  can  not  be  de- 
veloped at  a  profit  under  present  conditions  is  a  fact  which  in  many 
instances  is  learned  by  its  owner  only  after  a  large  and  unwarranted 
expense  is  entailed. 

323.  Purpose  of  Development. — Any  water  power  project  must 
be  examined  in  the  light  of  the  purposes  for  which  it  is  to  be  used 
or  the  market  it  is  to  supply.  The  supply  must  be  constant  and  con- 
tinuous not  only  for  every  day  in  the  year  but  for  every  year  of  its 
operation  unless  its  use  will  permit  of  the  discontinuation  of  the 
power  during  droughts,  high  water,  or  other  contingencies  that 
will  decrease  or  temporarily  suspend  the  generation  of  power  by  the 
plant. 

If  its  use  or  market  will  permit  of  such  interruption,  a  temporary 
power  may  sometimes  be  developed  to  advantage.  Where  the 
power  furnished  must  be  continuous  in  order  to  avoid  losses  or 
great  inconvenience,  precautions  must  be  taken  to  so  design  the 
plant  with  duplication  of  parts,  extra  units  and  suitable  pondage  or 


Cost  of  Development.  647 

storage  or  with  such  sufficient  auxiliary  sources  of  power  that  in- 
terruptions shall  be  essentially  obviated. 

In  some  cases  considerable  losses  have  been  entailed  by  hydraulic 
developments  constructed  without  sufficient  study  or  consideration 
of  these  questions.  In  such  cases,  the  plants  after  completion,  were 
unable  to  maintain  continuous  power,  without  the  installation  of 
auxiliary  steam  plants  for  use  during  the  temporary  interruptions 
to  which  the  plant  was  subject,  and  the  income  from  the  sale  of 
power  would  not  warrant  the  extra  expense  and  hence  the  plants 
were  commercial  failures. 

324.  Cost  of  Water  Power, — The  cost  of  water  power  depends  on : 
.    First:  The  investment  in  real  estate,  water  rights,  power  plant 
and  equipment,  transmision  lines,  sub-stations,  distribution  system, 
etc.,  and  the  interest  which  must  be  paid  thereon. 

Second :  On  the  loss  from  the  depreciation  of  the  various  elements 
of  the  plant,  the  cost  of  maintenance  and  repairs,  the  cost  of  con- 
tingent damages  from  floods  or  other  accidents. 

Third :  The  operating  expenses,  including  labor,  oil,  waste,  and 
other  station  supplies  and  expenses,  including  also  in,  hydro-electic 
plants,  the  patroling  and  maintenance  of  the  transmission  lines  and 
distribution  system. 

Fourth :  The  expenses  for  taxes,  insurance,  etc. 

The  total  annual  cost  due  to  the  above  sources  of  expense  is  the 
annual  cost  of  the  power  to  be  furnished  by  the  plant,  be  the  quan- 
tity of  that  power  much  or  little. 

The  investment  charge  should  be  liberally  estimated  and  should 
include  the  entire  expense  of  development  including  auxiliary  power 
plant,  if  needed.  All  contingencies  should  be  carefully  considered 
and  estimated.  A  serious  error  in  the  estimate  of  cost  caused  by 
large  and  unexpected  contingencies  in  construction  may  mean  a 
commercial  failure  of  the  enterprise.  The  same  consideration 
should  be  given  to  the  estimate  of  contingent  expenses,  deprecia- 
tion and  operating  expenses,  and  each  other  factor  on  which  the 
financial  life  of  the  plant  depends. 

325.  Cost  of  Development. — The  various  conditions  under  which 
water  power  is  developed  greatly  affect  the  cost  of  development. 
As  a  general  rule,  other  things  being  comparatively  equal,  the  larger 
the  power  developed  the  smaller  the  cost  of  development  per  unit 
capacity.     This  is  particularly  true  when  developments  of  various 
capacities  are  considered  on  the  same  stream.    Many  of  the  features 


648 


Cost,  Value  and  Sale  of  Power. 


of  the  development  must  be  essentially  the  same  regardless  of  the 
ultimate  capacity  of  the  plant.  This  is  especially  true  of  dams 
and  river  protection  work.  The  variation  in  cost  per  unit  capacity 
of  various  sized  plants  is  well  illustrated  by  Table  XLII. 

TABLE  XLII. 
Estimate  of  the  cost  of  a  Hydro- Electric  Plant  at  Niagara  Falls.* 


ITEMS. 

24-HouR  POWER  CAPACITY. 

50,000  H.  P. 
Development. 

75,  000  H.  P. 
Development. 

100,000  H.P. 
Develop- 
ment. 

Tunnel  tail-race  

$1,250,000 
450,000 
500,  000 
300,000 
1,080,000 
760,000 
350,000 
100,000 
75,000 

$1,250,000 
450,000 
700,  000 
450,000 
1,440,000 
910,000 
525,000 
100,  000 
75,  000 

$1,250,000 
450,000 
700,  000 
600,000 
1,980,000 
1,400,000 
700,  000 
100,  000 
75,000 

Headworks  and  canal 

Wheel  pit. 

Power  house  

Hydraulic  equipment  

Electric  eouipment 

Transformer  station  and  equipment.  . 
Office  building  and  machine  shop.  .  .  . 
Miscellao  eous 

Engineering  and  contingencies  10  per 
cent.  .  .    . 

$4,865,000 
485,000 

$5,900,000   - 
590,000 

$7,255,000 
725,000 

Interest,  2  years  at  4  per  cent  
Total  capital  cost 

$5,350,000 
436,  560 

$6,490,000 
529,584 

$7,980,000 
651,168 

$5,786,560 

$7,019,584 

$8,631,168 

Per  horse-power  

$114 

$94 

$86 

*  First  report  of  Hydro-Electric  Power  Commission  of  the  Province  of  Ontario, 
page  15. 

Other  things  being  comparatively  equal,  the  cost  of  development 
varies  inversely,  although  not  in  the  same  ratio,  as  the  head.  The 
reason  of  this  is  evident  from  the  fact  that  while  the  power  of  a 
stream  is  directly  proportional  to  the  head,  the  capacity  of  a  turbine 
increases  as  the  three-halves  power  of  the  head.  With  double  the 
head  the  power  of  a  wheel  is  increased  almost  three  times. 

For  moderate  changes  in  head,  the  cost  of  the  turbines  will  vary 
in  proportion  to  their  size  and  not  their  capacity ;  so  that  the  cost 
per  unit  of  capacity  will  usually  decrease  considerably  with  the 
head.  The  cost  per  unit  of  capacity  of  other  features  of  water  power 
plants  will  also  frequently  decrease  as  the  head  increases.  This  is 


Cost  of  Development. 


649 


particularly  true  of  pondage  capacity  which  increases  in  value 
•directly  as  the  head  increases,  although  the  cost  per  unit  of  land 
overflowed  may  remain  constant.  The  relative  cost  of  high  and 
low  head  developments  may  be  illustrated  by  the  comparative  cost 
of  two  plants  recently  designed  by  the  writer  which  were  of  ap- 
proximately the  same  capacity  but  working  under  different  heads. 
The  comparison  is  as  follows: 

TABLE  XLIII 
Comparative  Cost  of  Water  Power  Plants. 


COST  OF  WATER  POWER  DEVELOPMENT. 

Capacity. 

Head. 

Without 
dam. 

With 
dain. 

With  dam 
and  electrical 
equipment. 

With  dam,  electrical 
equipment  and 
transmission  line. 

8,000 

18 

63.50 

86 

115 

150 

8,000 

80 

21 

39 

60 

90 

TABLE  XLIV. 

Estimates  of  the  cost  of  developing  various  Comachian  power  from  Reports  of 
Ontario  Hydro- Electric  Power  Commission. 


Location  of  Proposed  Development. 

Natur- 
al 
head. 

Avail- 
able 
head. 

Power 
develop- 
ed, H.  P. 

Estimated 
capital 
cost. 

Cost 

£?. 

Cost  per 
H.  P.  per 
ft.  head. 

(1)  Healey's  Falls,  Lower  Trent  River  . 

00 

8000 

$675000 

§84  38 

Middle  Falls,  Lower  Trent  River 

30 

5200 

475000 

91  37 

Rauney's  Fall 

35 

6000 

425000 

69  67 

Rapids  above  Glen  Miller    .  . 

18 

3200 

3500CO 

109  38 



Rapids  above  Trenton  

18 

3200 

370000 

115  63 

•(2)  Maitland  River    

80  (5) 

1600 

325000 

203  12 

40 

1333 

250000 

187  53 

Beaver  River  (Eugenia  Falls) 

420 

2267 

291000 

128  28 

Severn  River  (Big  Chute)  

52  (6) 

4000 

350000 

87  50 

South  River  

85 

750 

115000 

153  33 

<3)  St.  Lawrence  River,  Iroquois,  Ont. 

12 

1200 

179000 

149  16 

Mississippi  River,-High  Falls,  Ont.  A 

78  (7) 

2400 

195000 

81  25 

Mississippi  River,  High  Falls.  Ont.  B 

78 

1100 

123000 

181  82 

* 

Montreal  River,  Fountain  Falls,  Ont. 

27 

2400 

214000 

89.16 

•(4)  Dog  Lake,  Kaministiquia  River  

347 

310  (8) 

13676 

832000 

61.00 

Cameron  rapids  

347 
39 

310 

6840 
16350 

619700 
815000 

91.00 
50  00 



39 

8250 

600000 

73  00 

Slate  Falls  

31 

40 

3686 

357600 

97  00 

31 

40 

1843 

260000 

141.00 

Third  Report;  (5)  Dam  rather  expensive.    (6)  Head  works  and  canal  less  expensive  than  ordin- 
ary.   (7)  With  storage  developed.    (8)  Including  3500  feet  of  head  water  tunnel. 


650 


Cost,  Value  and  Sale  of  Power. 


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652  Cost,  Value  and  Sale  of  Power. 

The  estimates  of  The  Ontario  Hydro-Electric  Power  Commission 
of  the  cost  of  various  hydro-electric  plants  proposed  in  Ontario, 
furnish  a  good  example  of  the  variations  in  the  cost,  per  unit  of 
power,  of  various  plants  under  various  conditions.  These  estimates 
are  shown  in  Table  XLIV. 

The  actual  costs  per  horse  power  capacity  of  various  complete 
American  and  foreign  plants  are  shown  in  Tables  XLV  and  XLVI, 
respectively. 

326.  Depreciation. — In    every    operating   plant    there    is    in   the 
course  of  time  a  certain  deterioration  or  reduction  in  value  due  to 
ordinary  operation  and  the  effect  of  the  elements.    In  the  considera- 
tion of  any  power  plant  as  an  investment,  allowance  must  be  made 
in  the  annual  charges  for  a  sum  sufficient  to  keep  the  original  in- 
vestment intact.     In  order  to  accomplish  this  an  allowance  should 
be  made  on  each  feature  of  the  plant  for  the  annual  reduction  in 
value  or  deterioration.    The  amount  of  depreciation  will  vary  with 
the  character  and  use  of  the  machinery  or  structure  and  shou,ld  be 
estimated  with  the  best  possible  knoweldge  of  the  conditions  under 
which  the  plant  will  be  operated,  fully  in  mind.     Such  estimates 
should  be  sufficiently  large  to  fully  cover  this  item  in  order  that  the 
feasibility  of  the  project  may  be  correctly  estimated. 

The  allowance  for  depreciation  in  an  operating  plant  should  be 
placed  in  a  sinking  fund  which  should  be  used  to  replace  the  vari- 
ous portions  of  the  plant  at  the  expiration  of  their  useful  life. 

327.  Annual  Cost  of  Developed  Power. — As  already  pointed  out 
the  annual  cost  of  operating  a  plant  includes : 

a.  Administration  and  operating  expense. 

b.  Maintenance  and  repairs. 

c.  Depreciation. 

d.  Interest,  insurance  and  taxes. 

Each  of  these  items  will  vary  with  the  duration  and  the  condi- 
tions under  which  the  power  plant  is  installed  and  operated.  The 
method  of  estimating  these  charges  in  shown  in  the  following  esti- 
mates of  the  cost  of  operation  of  the  Chicago  Sanitary  District 
Hydro-Electric  Plant  (see  Electric  World,  Feb.  28,  1906). 

Total  cost  of  development  and  transmission $3, 500, 000.00 

ESTIMATE  OF   COST. 

Interest  on  investment  at  4  per  cent $140,000.00 

Taxes  on  real  estate  buildings,  etc 7  260  00 

Depreciation  on  buildings  at  1  per  cent 3, 650 . 00 


Cost  of  Distribution.  653 

Depreciation  on  water  wheels  at  2  per  cent 2,027.32 

Depreciation  on  generators  at  2  per  cent 1, 824 . 60 

Depreciation  on  pole  line  at  3  per  cent 2,020.50 

Depreciation  on  other  electrical  appliances  at  3  per  ct.  3,995.52  


Total  fixed  charges , $161, 137.94 

OPERATING  EXPENSES. 

Power  and  sub-station  labor 63, 240.00 

Repairs  to  machinery  and  buildings 3, 700.00 

Incidental  expenses 1,200.00 

Operating  Lawrence  avenue  pumping  station 43, 960.00 

Operating  39th  avenue  pumping  station 120, 380.00 

Interest  on  investment  39th  avenue  pumping  station. .  15, 599 . 76 

248,079.76 


Total  cost  to  sanitary  district , $409, 217.70 

Capacity  15, 500  H.  P.     Cost  per  H.  P.  per  annum $26 . 40 

An  interesting  comparison  of  the  estimated  yearly  cost  of  various 
Hydro-Electric  generating  plants  is  given  in  the  various  reports  of 
the  Ontario  Hydro-Electric  Power  Commission  which  are  repro- 
duced in  Table  XLVII- 

328.  Cost  of  Distribution. — Having  estimated  the  annual  cost  of 
the  development  of  power  at  the  plant,  the  cost  of  distributing  the 
power  to  the  customer  must  also  be  considered.  In  many  power 
plants  the  power  is  generated  at  or  near  the  point  where  it  is  to 
be  used  and  the  transmission  losses  and  costs  will  include  its  trans- 
mission through  shafting,  cables,  and  belts,  or  by  electrical  means, 
to  the  machine  or  appliances  in  which  it  is  to  be  utilized.  In  other 
cases  the  power  has  to  be  transmitted  for  miles  by  high  voltage 
electric  currents.  The  units  of  power  for  which  the  power  com- 
pany will  receive  compensation  may  or  may  not  include  these 
various  transmission  losses.  Where  the  power  is  distributed  to  a 
factory,  the  losses  in  transmission  though  shafting,  belting,  etc.,  is 
usually  at  the  consumer's  expense ;  but  the  transmission  loss  in 
long  distance  lines  is  ordinarily  assumed  by  the  power  company 
and  must  be  taken  into  account  in  the  determination  of  the  cost  of 
furnishing  power  to  the  consumer.  The  losses  in  any  system  of 
distribution  are  a  considerable  element  of  the  cost  of  the  delivered 
power  and  must  be  carefully  estimated.  (Sec.  20,  page  24,  et  seq.) 

The  losses  in  the  distribution  of  power  in  various  mills,  factories, 
etc.,  as  determined  by  Prof.  C.  H.  Benjamin,  are  given  in  Table 
XLVIII.  The  reports  of  The  Ontario  Hydro-Electric  Power  Com- 
mission, to  which  references  have  already  been  made,  furnish  nu- 
merous clear  analyses  of  the  cost  of  electrical  distribution.  Table 


654 


Cost,  Value  and  Sale  of  Power. 


XLIX  shows  such  an  estimate  for  the  delivery  of  power  from  a 
proposed  Niagara  plant  to  a  proposed  sub-station  at  Hamilton, 
Ontario.  Table  L  shows  the  estimate  of  the  Commission  on  the 
cost  of  distributing  power  from  a  sub-station  to  an  individual  con- 
sumer not  within  the  local  distribution.  The  variations  in  the 
cost  of  power  from  the  generating  plant  to  the  consumer  is  also 
well  shown  by  Table  LI,  taken  from  the  same  source. 


TABLE  XLVIL 

Estimated   yearly   operating   expenses  of  generating   plant  from   Reports   of 
Ontario  Hydro-Electric  Power  Commission. 


Location  of  Plant. 

Horse-power. 

Net  H.  P.  trans- 
formed for 
transmisson. 

Operating  expen- 
ses including  - 
administration. 

Maintenance 
and  repairs. 

d 

.0 

a 

• 
Q 

Interest  at  4  per 
cent. 

Water  rental. 

1 

JO 

o 

j>> 

cS 

o> 

N 

Yearly  cost  of 
transformed 
24-hour  power.  1  1 

(1)  Niagara  plant 

r>oooo 

48750 

$57900 

$115700 

$86800 

$231400 

Sfi^OOn 

fijXM'.JAA 

fill      1C 

(2)  Middle  Falls.  .  . 

£5000 
100000 

5200 

73125 
97500 

4990 

70200 
86300 

11875 

140400 
172600 

9500 

105300 
129500 

9500 

280800 
345200 

19000 

6oOOO 
77500 

661700 
811100 

4W5 

9.05 
8.32 

10  00 

Healev's  Falls  

8000 

7680 

16875 

13500 

13500 

27000 

.  .  ... 

7087^ 

9  10 

Two  above  combined  

13200 

12670 

23000 

23000 

23000 

46000 

115000 

9  08 

(3)  Maitland  River  

1600 

5665 

2754 

2755 

13000 

24174 

Saugeen  River  

1333 

4840 

3247 

3->47 

9984 



21318 

Soutb  River   . 

750 

4100 

2620 

2620 

Severn  River  (Big  Chute) 
Severn  and  Beaver  Rivers 
combined  

4000 
6267 



17483 
23713 

8571 
13968 

8571 
14000 

14000 
25640 

485T5 

77000 

(4)  St.  Lawrence  River  

1200 

6864 

5119 

5118 

Mississippi   River   High 
Falls  

2400 

9391 

3840 

3841 

7777 

9AQAQ 

Mississippi    River   High 
Falls  

1100 

6390 

2491 

2491 

4908 

J0280 

Montreal   River    Fount- 
tain  Falls  

2400 

9850 

3903 

*21622 

cxqq 

(5)  Dog  Lake  

13675 

13760 

16127 

1  SQ?" 

6840 

13296 

1063-> 

10  13'^ 

04707 



Cameron  Rapids  

16350 

16375 

173'^7 

16727 

•  ••  

82.30 

14390 

11478 

10978 

24008 

60854 

Slate  Falls  

368(5 

6000 

H634 

1  &'W)'i 

1843 

6000 

3868 

3669 

10400 

23957 

( 

"Including  10-year  sinking  fund. 

To  make  the  delivered  current  available  for  power,  a  motor 
must  be  installed.  This  is  commonly  furnished  by  the  consumer. 
Table  LIT  shows  the  estimated  cost  of  induction  motor  service  per 
horse  power  per  year. 

329.  Effect  of  Partial  Load  on  Cost  of  Power.— The  maximum 
amount  of  work  that  any  plant  can  accomplish  will  be  done  only 
when  the  plant  works  to  its  full  capacity  for  twenty-four  hours  per 


Cost  of  Distribution. 


655 


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656 


Cost,  Value  and  Sale  of  Power. 


TABLE  XLIX. 

Showing  investments,  annual  charges,  and  cost  of  low  tension  power  at  sub- 
station.    (Sub-station  included.} 


Full  load. 

%  load. 

M  load. 

Total  horse'  power  distributed.  • 

16,000 

12,000 

8  000 

Total    investment,    including  step-down 
stations  and  interswitching. 

$450,879 

$404,  879 

$358,379 

Investment  per  H  P  delivered  

28  18 

33  73 

44  80- 

Total    annual  repairs,    depreciation,    pa- 
trolling and  operation  

22,  496 

19,092 

15,651 

Administration,  10  per  cent  of  repairs,  etc. 
Annual  interest,  4  per  cent  of  investment 

2,250 
18,035 

1,909 
16,  195  , 

1,565 
14,  335 

Total  annual  charges  

$42,  781 

$37,196 

$31,551 

Cost  of  24-hour  power,  including  line  and 
step-down  sub-station  losses  

$12  69 

$12  49 

$12  35- 

Cost  of  transmitting  and  transforming.  .  .  . 

2  67 

3  10 

3  94 

Total  cost  of  power  

$15  36 

$15  59 

$16  29- 

The  above  costs  of  power  are  based  on  an  assumed  rate  of  $12.00  per  24-hour 
horse-power  per  annum  for  high-tension  power  at  Niagara  Falls. 


TABLE  L. 

Showing   cost   of  distribution  from  municipal  sub-station  to  an  individual 
consumer,  not  covered  by  local  distribution. 


Distance  in 
miles  from 
municipal 
sub-station. 

COST  PER  HORSE-  POWER  PER  ANNUM  FOR  THE  DELIVERY 
OF  VARIOUS  AMOUNTS  OF  POWER. 

50  H.  P. 

75  H.  P. 

100  H.P. 

150  H.P. 

200  H.P. 

250  H.P. 

300  H.  P. 

2 

$5  58 
6  89 
7  92 
8  87 
10  20 

14  10 
16  12 

18  76  . 
22  74 

$4  20 
5  20 
6  18 

7  18 
8  24 

10  14 
12  13 

14  03 

17  08 

$3  53 
4  41 
5  20 

5  98 

6  77 

8  40 
9  54 

11  12 

13  48 

$2  92 
3  60 
4  27 
4  96 
5  38 

6  97 
8  31 

$2  74. 
3  25 
3  93 
4  55 
5  13 

6  24 

$2  60 
3  10 
3  72 
4  32 
•4  60 

5  79 
6  96 

7  96 

$2  511 
3  03  |  o  „; 
3  86^-g 
4  17  |  «  g 
4  43J 

SKJffs 
6  17  )  £  £ 

7  22  )  8% 
8  32  )  ®1 

3  

4... 

5  

6  . 

8... 

10  

7  68 

8  42 
9  35 

12  

10  12 
10  89 

15  

8  84 

Cost  of  Distribution. 


657 


TABLE  LI. 


COST  OF  24-HouR  POWER  PER  H.  P. 

PER  ANNUM. 


AMOUNT  OF  POWER  DELIVERED. 

At  Niagara 
Falls  includ- 

- 

ing  line  and 

At 

At 

step-  down 

sub-station. 

customer. 

sub  station 

losses. 

Full  load  2  000  H   P 

$18  54 

$21  89 

$26  03 

^  load  1  500  H  P 

13  18 

23  54 

29  06 

*•£  load  1  000  H  P 

12  85 

27  21 

34  48 

TABLE  LII. 
Capital  cost  and  annual  charges  on  motor  installations. 

Polyphase  25-cycle,  induction  motors. 


CAPACITY  H.  P. 

Capital 
cost  per 
H.  P. 
installed. 

ANNUAL  CHARGES. 

Interest 
5  per  cent. 

Deprecia- 
tion and 
repairs, 
6  per  cent. 

Oil,  care 
and 
operation. 

Total  per 
H.  P.  per 
annum. 

5  

$41  00 
39  00 
35  00 
28  00 
25  00 
24  00 
21  00 
20  00 
17  00 
16  00 

$2  05 
1  95 
1  75 
1  40 
1  25 
1  20 
1  05 
1  00 
85 
80 

$2  46 
2  34 
2  10 
1  88 
1  50 
1  44 
1  26 
1  20 
1*02 
96 

$4  00 
3  00 
2  50 
2  00 
1  75 
1  50 
1  25 
1  00 
80 
70 

$8  51 
7  29 
6  35 
5  28 
4  50 
4  14 
3  56 
3  20 
2  67 
2  46 

10  

15  

25 

35 

50 

75 

100 

150 

200                           . 

day.  Thus,  if  a  plant  has  a  capacity  of  one  thousand  horse  power 
and  is  operated  continuously  during  the  twenty-four  hours,  the 
total  output  will  be  twenty-four  thousand  horse  power  hours  of 
work.  Under  such  conditions  the  plant  can  be  built  at  a  minimum 
expense  per  unit  of  output  and  the  cost  of  operation,  fixed  charges, 
interest,  etc.,  will  be  less  per  unit  of  work  done  than  under  any 
other  condition  of  operation. 
40 


658  Cost,  Value  and  Sale  of  Power. 

For  example :  If  a  plant  of  one  thousand  horse  power  be  installed 
at  a  cost  of  one  hundred  thousand  dolars,  the  annual  cost  of  opera- 
tion, including  fixed  charges  and  all  other  legitimate  expenses,  may 
be  estimated  as  follows : 

Interest  on  $100, 000  at  6  per  cent $  6, 000 

Repairs  and  depreciation ~.l   5, 300 

Operating  expenses 10, 000 

Miscellaneous  and  contingent  expenses 4, 250 

Total  annual  cost  of  power $25, 550 

On  the  above  basis  the  annual  cost  for  each  horse  power  of  maxi- 
mum load  will  be  $25.55.  If  the  plant  works  at  its  maximum  capac- 
ity for  twenty-four  hours  per  day,  the  cost  per  horse  power  hour 
will  be  .292  cts.  If,  however,  the  plant  is  operated  to  its  full  capac- 
ity for  12  hours  per  day  only,  the  total  Cost  of  power  may  be  reduced 
to  say  $23,000  per  annum.  In  this  case  the  cost  per  horse  power 
of  maximum  load  will  be  reduced  to  $23.00  per  year,  but  the  cost 
per  horse  power  hour  of  energy  generated  will  be  increased  to 
.526  cts.  In  many  cases  the  plant  will  be  used  for  ten  hours  per 
day  and  for  six  days  per  week.  Its  maximum  capacity  may  be 
utilized  only  occasionally,  and  the  demand  for  power  will  vary 
greatly  from  haur  to  hour  resulting  in  a  load  factor  of  perhaps  50 
per  cent,  or  less.  In  this  case  the  annual  cost  per  maximum  horse 
power  will  still  not  exceed  twenty-three  dollars  ($23))  per  year, 
.but  the  annual  cost  of  average  ten  hour  power  will  be  forty-six 
dollars  ($46),  and  the  cost  per  horse  power  hour  of  useful  work  will 
be  increased  approximately  to  1.5  cents.  The  cost  of  each  unit  of 
power  under  the  last  condition  is  over  five  times  as  great  as  in  the 
first  case  mentioned,  and  about  three  times  as  great  as  in  the  second 
case  discussed.  It  is  therefore  obvious  that  unless  the  conditions 
of  use  are  carefully  studied  and  conservatively  estimated,  they  may 
lead  to  unfortunate  investments  and  financial  losses. 

330.  Cost  of  Auxiliary  Power,  or  Power  Generated  From  Other 
than  Water  Power  Sources. — It  frequently  becomes  necessary  to  es- 
timate the  cost  of  power  plants  and  of  power  developed  from  other 
than  water  power  sources.  This  is  necessary  in  order  to  determine 
the  probable  cost  of  auxiliary  power  plants  and  such  auxiliary 
power  as  may  be  needed  to  assist  a  water  power  plant  at  times 
when  the  hydraulic  power  is  deficient.  It  is  also  necessary  to  deter- 
mine the  cost  of  power  with  which  the  hydraulic  plant  may  be 
called  upon  to  compete. 


Cost  of  Auxiliary  Power. 


659 


For  a  correct  estimate  of  such  cost,  it  is  necessary  to  determine 
the  efficiency  of  the  various  parts  of  the  plant  (see  page  31)  under 
all  conditions  o<f  operation  in  order  to  correctly  determine  the  actual 
cost  of  power  due  to  the  conditions  of  operation.  The  conditions  for 
maximum  efficiencies  are  seldom  met  in  actual  operation,  and  the 
cost  of  generating  the  power  is  increased  by  the  irregularities  of 
operating  conditions.  In  all  power  plants  the  effect  of  partial  or 
irregular  load  affects  the  cost  of  power  in  the  same  manner  as  al- 
ready described  in  Section  328. 


Fixed  Charges 

Operating  Expenses. 


1000  1500 

Morse  Power  of   Plarrt-. 


2500 


Fig.  399.  Cost  of  Steam  Power  per  Horse  Power  per  Annum  in  Various 

Plants. 

By  far  the  largest  amount  of  power  generated  is  from  fuel  and 
by  steam  plants.  The  cost  of  the  development  of  steam  power  is 
modified  by  the  cost  and  character  of  coal  used ;  the  size  and  char- 
acter of  the  machinery  operated ;  the  character  of  the  load  (that  is, 
the  load  factor)  ;  the  number  of  hours  during  which  the  plant  is  used 
per  year ;  and  the  skill  and  ability  of  the  engineer  and  fireman  who 
have  charge  of  the  plant.  Observations  of  the  actual  cost  of  de- 


66o 


Cost,  Value  and  Sale  of  Power. 


veloping  power  must  therefore  form  the  basis  of  any  accurate  esti- 
mate of  the  cost  of  power  production. 

Mr.  H.  A.  Foster*  made  actual  tests  of  twenty-two  different 
power  plants,  including  manufacturing  establishments,  electric 
light  stations,  pumping  plants,  etc.,  and  determined  for  each  plant 
the  power  consumption  per  annum  and  its  cost,  including  not  only 
running  expenses  but  fixed  charges.  The  cost  per  horse  power  per 
annum  varied  from  a  minimum  of  $15.69  to  a  maximum  of  $233.95. 

TABLE  LIU. 

Showing  average  power  developed  and  its  cost  per  HP.  in  22  steam  power 

plants. 


OUTPUT. 

Operating  ex- 
penses, per 
HP. 

Fixed 
charges,  per 
H.  P. 

Total  cost, 
HP.  per 
annum. 

Cost  per 
HP.  hr., 
cts. 

Average  HP. 
developed. 

No.  of 
days  per 
annum. 

12.4 

361 

$147.93 

$25.40 

$173.33 

5.648 

20.9 

365 

123.12 

28.42 

151.54 

]  .  868 

21.5 

361 

90.47 

17.80 

108.27 

2.918 

32.9 

330 

22.56 

5.83 

28.39 

.832 

36.7 

365 

137.25 

96.70 

233.95 

2.811 

42.4 

365 

86.38 

63.20 

149.58 

1.708 

53. 

309 

56.94 

19.51 

76.45 

1-.696 

58.8 

365 

97.30 

33.82 

131.12 

1.613 

70.4 

365 

101.69    ' 

20.78 

122.45 

1.641 

129.3 

365 

30.14 

9.41 

39.55 

.S71 

166.7 

313 

15.19 

4.47 

19.66 

.639 

173. 

313 

22.66 

5.83 

28.39 

3.333 

210.9 

290 

40.33 

7.86 

48.19 

.693 

296.7 

^97 

45.56 

7.81 

53.37 

.74'.) 

926. 

307 

11.73 

8.77 

20.50 

.691 

1,010.8 

306 

15.70 

7.74 

23.44 

.794 

1,174.8 

306 

10.19 

5.50 

15.69 

.531 

1,278.7 

293 

10.49 

6.23 

16.72 

.590 

1,345.5 

365 

23.28 

9.42 

32.70 

.820 

1,352. 

365 

33.03 

29.41 

62.44 

.713 

1,909.7 

306 

13.40 

6.63 

20.03 

.677 

2,422 

306 

15.67 

6.73 

22  40 

.757 

A  summation  of  the  results  of  these  observations  is  shown  in  Table 
LIII  and  the  plotted  results  of  the  table  are  shown  in  Fig.  399. 
Mr.  R.  W.  Conant**  determined  the  operating  expenses  of  various 
street  railway  power  stations  and  compiled  a  table  (see  Table  LIV 
which  gives  important  information  bearing  on  this  question. 


*  See  Trans.  Am.  Inst.  E.  E.  Vol.  14,  p.  385. 
**  See  Engineering  News,  Vol.  40,  p.  181. 


Cost  of  Auxiliary  Power. 


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662 


Cost,  Value  and  Sale  of  Power. 


An  important  discussion  of  the  effect  of  the  load  factor  on  the 
cost  of  power  was  recently  made  by  Mr.  E.  M.  Archibald. -f  This 
discussion  was  accompanied  by  various  diagrams  which  illus- 
trate clearly  the  principles  involved.  Two  of  these  diagrams  are 
reproduced  in  Figs.  400  and  401.  The  diagrams  are  so  complete 
as  to  need  no  further  description.  The  additional  diagrams  and 


.9  a 

Fig.  400. -Operating  Expense  of  a  900  K.  W.  Condensing  Steam  Plant 
with  a  750  K.  W.  Peak. 

the  descriptive  matter  in  the  paper  itself  should  be  carefully  studied 
in  this  connection. 

Table  LV  shows  the  capital  costs  of  steam  power  plants  of  var- 
ious capacities  and  the  annual  cost  of  power  per  brake  horse  power 
as  estimated  by  The  Ontario  Hydro-Electric  Power  Commission. 
fSee  Electrical  Age,  Nov.,  1906. 


Market  Price  of  Water  Power. 


663 


Similar  costs  for  producer  gas  power  are  shown  in  Table  LVI  from 
the  same  source,  and  the  Commission's  estimate  of  the  effect  on 
the  cost  of  power  oif  variations  in  the  price  of  coal,  is  shown  in 
Table  LVIL 

331.  Market  Price  of  Water  Power. — The  market  price  of  water 
power  must  be  predicated  on  two  considerations:  First:  The 
price  at  which  the  Power  Company  can  afford  to  furnish  power  and 
insure  a  fair  return  of  its  investment,  and,  Second :  The  price  that 
the  consumer  can  afford  to  pay  for  the  power.  The  latter  amount 


Fig.  401.— Ratio  of  individual  Items  of  Expense  to  Total  Operating  Expense 
of  a  900  K.  W.  Condensing  Steam  Plant  With  a  750  K.  W.  Peak. 

is  commonly  fixed  by  what  it  will  cost  to  produce  the  power  by 
some  other  means. 

If,  in  the  preliminary  investigation  of  a  water  power  project,  it 
is  found  that  the  cost  to  the  Power  Company  of  generating  power 
will  be  greater  than  the  price  at  which  the  power  can  be  sold,  it  is,  of 
course,  evident  that  the  plant  will  be  a  financial  failure,  and  the 
scheme  should  at  once  be  abandoned.  In  introducing  a  new 


664 


Cost,  Value  and  Sale  of  Power. 


TABLE  LV. 

Showing  capital  costs  of  steam  plants  installed  and  annual  costs  of  power 

per  brake  horse-power. 


SIZE  OF  PLANT 
H.  P. 

CAPITAL  COST  OF  PLANT  PER  H.  P. 
INSTALLED. 

Annual  cost 
of  10-hour 
power  per 
B.  H.  P. 

Annual   cost 
of  24-hour 
power  per 
B.  H.  P. 

Engines, 
boilers,  etc., 
installed. 

Buildings. 

Total. 

CLASS  I.— Engines:  simple,  slide-valve,  non-condensing.     Boilers:  return 

tubular. 


10 

$66  00 

$40  00 

$106  00 

$91  16 

$180  76 

20  

56  00 

37  00 

93  00 

76  31 

151  48 

30  

48  70 

35  00 

83  70 

66  46 

131  68 

40 

44  75 

33  50 

78  25 

59  46 

117  74 

50  . 

43  00 

31  00 

74  00 

53  95 

106  46 

CLASS  II.— Engines:  Simple,  Corliss,  non-condensing.      Boilers:  Return  tubular. 


30 

$70  70 

$35  00 

$105  70 

$61  14 

$117  70 

40  
50  

62  85 
59  00 

33  50 
31  00 

96  35 
90  00 

55  50 
50  70 

107  10 
97  73 

tiO  

56  00 

30  00 

86  70 

47  42 

91  34 

80  

50  00 

27  50 

77  50 

43  86 

85  41 

100 

44  60 

25  00 

69  60 

40  55 

79  19 

CLASS  III.— Engines:  Compound,  Corliss,  condensing. 

with  reserve  capacity. 


Boilers:  Return  tubular, 


100  

$63  40 

$28  00 

$91  40 

$33  18 

$60  05 

150  

53  70 

24  00 

77  70 

29  83 

54  63 

200  

50  10 

20  00 

70  10 

28  14 

51  72 

300 

45  90 

18  00 

63  90 

26  27 

48  83 

400...  
500  
750  

43  55 
41  25 

40  50 

16  00 
14  00 
13  00 

59  55 
55  25 
53  50 

24  84 
23  73 
23  56 

46  12 
44  21 
44  0'? 

1,000  

39  00 

12  00 

51  00 

23  26 

43  71 

CLASS  IV.  — Engines:  Compound,  Corliss,  condensing.     Boilers:  Water-tube, 
with  reserve  capacity. 


300.. 
400  

$55  20 
51  50 

$18  00 
16  00 

$73  20 
67  50 

$25  77 
24  18 

$46  32 
43  61 

500  

49  40 

14  00 

63  40 

23  19 

42  03 

750 

46  80 

13  00 

59  70 

22  88 

41  56 

1,000 

44  30 

12  00 

56  80 

22  47 

41  11 

NOTE.  — Annual  costs  include  interest  at  5  per  cent,  depreciation  and  repairs  on 
plant,  oil  and  waste,  labor  and  fuel,  (coal  at  $4.00  per  ton). 
Brake  horse-power  is  the  mechanical  power  at  engine  shaft. 


Cost  of  Auxiliary  Power. 


665 


TABLE  LVI. 

Showing  capital  costs  of  producer   gas  plants   installed   and   annual   costs  of 
power  per  brake  horse-power. 


SIZE  OF  PLANT,  H.  P. 

CAPITAL  COST  OP  PLANT  PER 
H.  P.  INSTALLED. 

Annual 
cost  of 
10-hour 
power  per 
B.  H.  P. 

Annual 
cost  of 
24-hour 
power 
per 
B.  H.  P. 

Machine'y 
etc. 

Buildings. 

Total. 

10 

$137  00 
110  00 
93  00 
84  50 
80  00 
79  00 
78  20 
77  50 
76  00 
74  00 
73  00 
71  50 
70  00 
67  50 
65  00 

$40  00 
36  00 
33  00 
29  00 
26  00 
24  00 
22  00 
20  00 
19  00 
17  00 
16  00 
14  00 
12  00 
10  00 
8  00 

$177  00 
146  00 
126  00 
113  50 
106  00 
103  00 
100  20 
97  50 
95  00 
91  00 
89  00 
85  50 
82  00 
77  50 
73  00 

$53  48 
44  47 
38  73 
85  05 
32  27 
30  49 
28  70 
27  05 
25  87 
24  95 
24  24 
23  41 
22  54 
.21  55 
20  46 

$90  02 
75  22 
65  99 
59  85 
55  22 
52  03 
48  95 
45  40 
43  17 
41  78 
40  40 
39  03 
37  54 
35  99 
34  66 

20 

30 

40 

50           ... 

60       

80       

100    

150    

200  

300  

400  .'. 

500 

750  

1  000 

NOTE. — Annual  costs  include:  interest  at  5  per  cent,  depreciation  and  repairs 
on  pliant,  oil  and  waste,  labor  and  fuel  (Bituminous  coal  at  $4.00  and  Anthra- 
cite coal  at  $5.00  per  ton). 

TABLE  LVI1. 

Showing  the  effect  on  the  cost  of  power  of  a   variation  in  the  price  of  coil  of 

one-half  dollar  per  ton. 


Size  of  Plant. 

SUCTION 
PRODUCER  GAS. 

STEAM. 

10 
Hour. 

24 
Hour. 

10  Hour. 

24 
Hour. 

10 

$1  15 
1  13 
1  10 
1  07 
1  04 
1  01 
98 
96 
94 
92 
90 
88 
86 
82 
76 

$2  53 
2  46 
2  40 
2  33 
2  29 
2  24 
2  18 
2  12 
2  07 
2  02 
1  98 
1  94 
1  89 
1  81 
1  72 

Simple  automat-  | 
ic  non-condes-<( 
inof  . 

P6  14 
5  25 
4  71 
3  56 
3  37 
3  26 
3  15 
3  12 
1  75 
1  69 
1  62 
1  56 
1  39 
1  39 
1  39 

$13  47 
11  56 
10  35 
7  84 
7  41 
7  16 
6  97 
6  87 
3  85 
3  71 
3  60 
3  44 
3  05 
3  05 
3  05 

20 

30                            . 

40                      

50               

60  

80  

100 

Compound    con-J 
densing              1 

150 

200 

300. 

400                

[ 

Compound    con-  f 
densing  water-  •] 
tube  boilers.  .  .  ( 

500             

750  

1000  

666  Cost,  Value  and  Sale  of  Power. 

source  of  power  into  any  community  where  the  power  introduced 
will  be  obliged  to  compete  with  other  sources,  it  can  seldom  be 
expected  that  the  power  to  be  so  furnished  can  be  sold  at  the  same 
price  as  the  power  already  on  the  market.  It  is  at  least  only  safe 
to  estimate  that  the  power  must  be  sold  at  a  somewhat  lower  figure. 
If  the  power  already  in  use  is  sold  or  generated  at  a  profit,  a  cut 
in  price  may  be  anticipated  from  the  competing  company ;  and,  in 
the  second  place,  as  a  considerable  expense  is  necessarily  involved 
in  the  change  of  apparatus,  etc.,  necessary  to  utilize  a  new  source  of 
power,  consumers  will  be  slow  to  make  such  changes  unless  they 
can  do  so  to  a  considerable  financial  advantage. 

In  calculating  the  cost  of  power  to  a  consumer,  if  he  undertakes 
to  generate  it  himself,  the  fair  cost  should  be  based  upon  interest, 
depreciation,  operation,  etc.,  of  the  plant  which  is  necessary  to  be 
installed.  If,  however,  the  consumer  has  such  a  plant  already  in- 
stalled, no  further  investment  is  necessary,  and  as  the  machinery 
installed  can  not  be  sold  to  advantage,  the  investment  charges  or 
the  fixed  charges  on.  such  a  plant  can  not  be  considered,  and  the 
consumer  will  make  a  change  in  power  only  provided  the  power 
can  be  furnished  from  the  new  source  at  or  below  the  actual  cost 
of  generation  in  his  own  plant,  or  at  such  additional  cost  as  the 
convenient  reliability  of  other  desirable  features  of  the  new  source 
of  power  will  warrant. 

In  estimating  the  price  at  which  the  consumer  can  afford  to  pur- 
chase power,  not  only  the  price  at  which  power  is  no\v  sold  but 
any  possible  decrease  in  the  sale  price,  due  to  competition  or  to 
other  and  more  economical  developments,  must  be  considered. 
Better  and  more  economical  machinery  in  local  plants,  or  water 
powers  that  are  nearer  the  market  and  that  can  be  developed  or 
operated  at  less  expense,  may  so  reduce  the  market  price  as  to  ser- 
iously affect  the  value  of  power,  and  hence  the  probability  of 
the  development. 

332.  Sale  of  Power. — Attention  has  already  been  called  to  the 
fact  that  if  the  capacity  of  a  plant  can  be  used  for  only  a  portion  of 
the  time,  the  cost  of  the  development  per  unit  of  power,  and  there- 
fore the  cost  per  unit,  is  very  greatly  increased.  This  is  a  matter 
of  the  greatest  importance  'which  should  be  kept  clearly  in  mind  in 
the  sale  power.  The  load  factor  of  many  users  is  comparatively 
low.  Most  companies  organized  for  the  general  sale  of  electrical 
power  in  municipalities  have  a  load  factor  of  35%  or  less.  A  sale 
of  power  to  such  consumers,  to  be  used  under  such  conditions,  is 


Sale  of  Power.  667 

liable  to  very  greatly  increase  the  cost  of  power  to  the  power  com- 
pany, especially  if  the  maximum  power  to  be  furnished  is  large  as 
compared  with  the  total  capacity  of  the  plant.  For  example:  If, 
in  a  3,000  horse  power  plant,  power  is  sold  on  a  horse  power  hour 
basis,  with  a  peak  load  of  1,000  horse  power  and  a  load  factor  of 
30%,  the  average  twenty-four  hour  power  furnished  to  the  con- 
sumer will  be  only  300  horse  power,  while  the  total  peak  that  the 
power  plant  will  be  called  upon  to  carry  at  any  time'  will  be  1,000 
horse  power  or  one-third  of  the  total  capacity  of  the  power  plant. 
With  such  sale  of  power  the  power  plant  is  likely  to  be  seriously 
handicapped.  With  power  sold  in  such  large  blocks,  the  overlap- 
pings  of  the  peak  loads  can  not  reasonably  be  expected  to  compen- 
sate for  each  other.  The  net  results  of  such  a  sale  will  be  that  the 
company  has  tied  up  one-third  of  the  capacity  of  its  plant  but  will 
receive  payment  for  only  one-tenth  of  its  capacity.  It  is  evident 
that  unless  such  conditions  are  realized  and  such  a  charge  is  made 
for  power  as  will  compensate  the  power  company  for  the  same, 
the  power  company  may  readily  tie  up  its  entire  out-put  and  yet 
not  receive  50%  of  the  income  that  should  be  reasonably  antici- 
pated. If,  on  the  other  hand,  the  sale  of  power  is  made  in  small 
blocks,  or  to  small  consumers,  it  is  frequently  possible  to  greatly 
over-sell  the  total  capacity  of  the  plant  and  yet  take  care  of  the 
consumers  in  a  satisfactory  manner.  That  is,  on  account  of  the 
overlapping  of  the  peak  loads  and  the  equalization  of  the  load  car- 
ried throughout  the  twenty-four  hours,  the  total  connected  load 
sold  may  often  considerably  exceed  the  capacity  of  the  plant.  For 
example :  In  one  water  power  plant,  having  a  total  capacity  of 
about  4,000  horse  power,  the  actual  connected  load  is  over  10,000 
horse  power.  In  many  power  plants  the  actual  connected  load  is 
two  or  three  times  the  plant's  capacity.  It  is  evident,  however, 
that  such  a  condition  can  exist  only  with  small  consumers,  and  that 
where  a  single  consumer's  load  is  a  large  fraction  of  the  plant's 
capacity,  it  will  not  only  be  impossible  to  overload  the  power  plant, 
but  in  addition  extra  machinery  must  always  be  installed  to  supply 
the  demand  should  any  accident  happen  to  the  regular  installation. 

Mr.  E.  W.  Lloyd  has  compiled  some  valuable  data  concerning 
the  power  loads  on  various  central  states  from  various  classes  of 
consumers.  This  data  is  given  in  Table  LVIII. 

The  increase  in  the  charges  for  power  to  consumers  on  account 
of  the  variation  in  power  factor  is  well  illustrated  by  Fig.  402  taken 
from  the  paper  of  Mr.  Archibald  before  referred  to. 


668 


Cost,  Value  and  Sale  of  Power. 


TABLE  LVIII. 

Actual  conditions  under  which  power  is  furnished  to  consumers  from  Central 

Stations. 


Character  of  Installations. 


dual 
p  d 


rcentage  of  aver 
ge  load  to  con- 
ected motor 


Bakeries 1582 

Bakeries 705.3 

Boiler  shops 326.7 

Boiler  shops 1172 

Boots  and  shoes 3050 

Box  making 1555 

Blacksmiths 586 

Brass  finishing 5736 

Butchers  and  packers 1990 

Butchers  and  packers 1U49 

Breweries 12310 

Carpet  cleaning 644 

Cement  mixing 2009 

Candy  manufactory 1893 

Candy  manufactory 796 

Cotton  mills 11829 

Carriage  works 2091 

Chemical  works 4802 

Clothing  manufacturing 1 181 

Grain  elevators 3842 

Feather  cleaners 2447 

•General  manufacturing 6133 

Engraving  and  electrotyping 863 

Engraving  and  electrotyping 2369 

Glass  grinding 2760 

Foundries 2057 

Foundries 2419 

Furniture  manufacturing 1750 

Flour  mills 41276 

Hoisting  and  conveying 2905 

Hoisting  and  conveying 0562 

Ice  cream 596 

Refrigeration 4645 

Jewelry  manufacturing 2526 

Laundries 676 

Marble  finishing 1464 

Machine  shops I  4006 

Newspapers 3150 

Newspapers 4975 

Ornamental  iron  works 2771 

Paint  manufacturing 281 4 

Printers  and  bookbinders 1147 

Printers  and  bookbinders 6215 

Plumbing,  manufacturing 3020 

Rubber  manufacturing 1051 

Sheet  metal  manufacturing 1321 

Soap  manufacturing 3434 

Seeds 2917 

Structural  steel 6514 

Structural  steel 77704 

Stone  cutting 7425 

Tanners 2466 

Tobacco  working 3441 

Wholesale  groceries 2005 

Wood  working 2306 

Woolen  mills 20985 

Averages 3500 


32.8 
22.5 
51.4 
32.2 
39.7 
18.1 
9.4 
40.5 
24.8 
3ti.9 
94.0 
14.5 
37.5 
26.6 
29.9 
99.0 
24.8 

109.0 
23.0 

114.4 
54.4 
67. H 
12.4 
46.3 
33.5 
27.7 
81.1 
35.7 

148.5 
70.5 

253.0 
31.0 
36.7 
31.7 
10.8 
19.8 
57.6 
47.4 

137.0 
38.4 
60.4 
20.4 
76.8 
42.4 
26.0 
38.8 
73.0 
55.1 

176.0 

552.1 
76.5 
28.6 
62.3 
47  0 
39.5 

150.0 


Group 
Individual 
G 
I 
G 
G 
G 
G 
G 
I 
G 
G 

G 

I 

G 

G 

G 

G 

G&I 
G&I 
G&I 

G 

I 

G 

G 

I 

G 

G 

G 

I 

G&I 
GGI 

G 
G&I 

G 

G 

I 

G 
G&I 

G 

I 

G 
G&I 

G 

G 
G&I 

I 

G 
G&I 

G 

G 

G  &I 
U  &I 


2.7 
3.1 
2.8 
5.2 
5.8 
4.3 
2.2 
7.4 
2.0 
6.7 
4.6 
1.6 
1.0 
3.5 
7.5 
3.0 
3.5 
5.5 
4.0 
3.8 
5.5 
6.4 
2.5 

26.7 
3.0 
2.3 
7  0 
3.6 
3.1 
6.4 

20.0 
5.4 
2  5 
4.6 
2.1 
1.3 
4.5 
4.8 

17.3 
3.6 
4.6 
2.6 

24.0 
4.8 

15.0 
3.7 

10.0 
5.8 

16.1 

35.6 
3.8 
2.6 
7.0 
4.5 
3.6 
3.0 


6.08 


27.8 
19.5 
33.3 
20.7 
42.8 
45.4 
34.2 
45.0 
36.4 
18.8 
33.0 
30.1 
24.9 
33.6 
16.3 
60.1 
35.5 
23.5 
44.5 
32.6 
25.7 
33.9 
46.9 
22.5 
36  6 
43.7 
21.3 
35.6 
48.1 
28.3 
13.0 
35.9 
53.4 
31.6 
34.0 
51.3 
34.5 
38.0 
15.1 
41.6 
26.5 
39.5 
26.0 
21.5 
24.7 
27.3 
27.6 
24.4 
18.5 
31.1 
34.4 
54.6 
37.5 
26.0 
33.3 
71.0 

33.9 


An  Equitable  Basis  for  the  Sale  of  Power. 


669 


333.  An  Equitable  Basis  for  The  Sale  of  Power. — It  is  there- 
fore essential,  in  order  to  establish  an  equitable  basis  for  the  sale 
of  power,  that  some  additional  factor  besides  the  units  of  power 
furnished  be  considered  in  determining  the  basis  for  the  prices 
charged.  One  of  the  most  equitable  bases  for  the  sale  of  power 


70 


60 


5.0 


30 


t 


I 


Fig.  402.— Cost  of  Steam-Generated  Electric  Power  to  the  Consumer. 

is  apparently:  First:  A  service  charge  to  the  consumer  of  a  fixed 
price,  based  on  the  peak  load  carried ;  Second :  To  this  should  be 
added  a  price  for  the  units  of  power  actually  furnished.  The  fixed 
price  should  equal  the  interest,  depreciation,  etc.,  on  the  capacity 
that  is  to  be  provided  or  set  aside  to  carry  the  peak  load  of  the 
customer.  The  unit  price  for  power  should  be  an  equitable  charge 
for  the  quantity  of  power  which  will  actually  be  sold.  Where  both 


670  Cost,  Value  and  Sale  of  Power. 

of  these  quantities  are  fixed,  a  net  price  per  horse  power  per  year, 
or  a  total  price  per  annum  for  the  power  to  be  furnished,  can,  of 
course,  be  arranged  equitably.  The  main  idea  in  establishing  a 
price  for  power  is  to  keep  clearly  in  mind  the  factors  that  enter 
into  the  sale  of  power,  so  that  in  making  a  contract  for  the  use  of 
power  the  rights  of  both  power  company  and  consumer  shall  be 
duly  considered.  The  sale  of  power  at  a  profit  is  one  of  the  most 
essential  features  in  the  management  of  the  power  plant,  and  many 
plants  have  been  wholly  or  partially  financial  failures  on  account 
of  the  ignorance  of  the  basic  principle  on  which  power  should  be 
sold. 

The  method  of  charging  for  power  outlined  above  is  illustrated  by 
the  charges  for  Electric  Current  furnished  from  Niagara  Falls,  by 
the  Cataract  Power  &  Condu.it  Co.  of  Buffalo,  as  given  in  the  En- 
gineering News  (May  26th,  1898)  as  follows : — 

"All  payments  for  power  are  to  be  made  monthly  and  the  amount 
of  each  monthly  payment  will  consist  of  a  charge  for  service,  and 
in  addition  thereto,  a  charge  for  power.  The  charg,e  for  service 
is  $i  per  kilowatt  per  month,  and  this  charge  will  depend  omly 
upon  the  amount  of  power  which  the  user  may  require  the  Catar- 
act Power  &  Conduit  Company  to  keep  available  and  ready  for  his 
use.  The  monthly  charge  for  power  will  depend  upon  the  aggre- 
gate amount  used,  as  determined  by  integrating  meters  installed 
by  the  Conduit  Company  upon  the  premises  of  the  consumer.  The 
charge  for  power  will  be  determined  from  the  following  schedule : — 

Units  (K-W.  hrs.}  used  Charge  pzr  unit 

per  month.                                      For  current  up  to  For  the  excess. 

Up  to  1,000                                        1,000  units,  2.0    cts.  2.0    cts. 

l,000to    2,000                       1,000  units,  2.0    cts.  1.5    cts. 

2,000  to    3,000                       2, 000  units,  1.5    cts.  1.2    cts. 

3,000  to    5,000                      3, 000  units,  1.2    cts.  1.0    cts. 

5,000  to  10,000                       5, 000  units,  1.0    cts.  0.8    cts. 

10, 000  to  20, 000  10, 000  units,  0 . 8    cts.  0-75  cts. 

20, 000  to  40, 000  20, 000  units,  0 . 75  cts.  0. 70  cts. 

40, 000  to  80, 000  40, 000  units,  0 . 70  cts.  0 . 66  cts. 

Over  80,000  80,000  units,  0.66  cts.  0.64  cts. 

334.  Value  of  Improvements  Intended  to  Effect  Economy. — In 
many  plants  the  first  cost  of  an  installation  is  an  important  matter 
and  must  sometimes  have  a  greater  effect  than  the  interest  and  de- 
preciation charge  would  seem  to  warrant.  In  most  cases  the  plan 
should  be  studied  in  detail  and  improvements  introduced  or  re- 


Value  of  a  Water  Power  Property.  671 

jected  on  the  basis  of  their  true  financial  value.     Such  considera- 
tion should  usually  be  made  on  the  following  basis : 

Dr. 

Invest  required  to  effect  improvement. ...  $ 

Interest  on  investment $ 

Depreciation  on  improvements 

Extra  expense  of  operation  and  mainten- 
ance   $ 


Total  annual  cost  of  improvement . .  $ 

.0. 

Saving  in  power  (or  in  expense)  effected 

by  improvement     $ 

Annual  value  of  saving  effected $ 

Net  annual  gain  or  loss  .due  to  im- 
provement   $ 

Capitalized  value  of  power  (or  expense) 

effected  by  improvement  $ 

Net  capitalized 'loss  or  gain  effected  $  

335.  Value  of  a  Water  Power  Property. — It  has  frequently  be- 
•come  necessary  in  this  country  to  condemn  water  power  privileges 
on  account  of  the  necessity  of  securing  public  water  supplies  or 
for  other  public  purposes.  Under  such  conditions  it  frequently  be- 
comes necessary  to  estimate  the  value  of  the  water  power  property. 
When  such  matters  are  brought  into  court  and  various  witnesses 
are  heard  on  the  subject,  it  is  commonly  found  that  very  great  dif- 
ferences of  opinion  exist  as  to  the  value  of  power-  These  differ- 
•ences  of  opinion  are  largely  the  result  of  entirely  different  points  of 
view. 

To  those  who  have  carefully  followed  the  discussion  of  the  hy- 
drograph,  and  the  estimate  of  power  based  thereon,  the  great  var- 
iations that  occur  in  the  potential  power  of  streams  at  various 
times  in  the  season,  and  in  the  various  years,  are  obvious. 

It  is  apparent  that  different  engineers,  even  if  they  take  carefully 
into  account  these  variations  in  power,  may  differ  very  greatly  in- 
deed as  to  the  extent  to  which  the  power  can  be  economically  de- 
veloped. 

The  question  of  pondage  as  discussed  in  Chap.  XXVI  also  has 
a  very  important  bearing  on  this  matter.  It  is  only  by  a  careful 
study  of  the  whole  question  and  the  consideration  of  the  power 
market  that  even  an  approximately  correct  answer  to  this  question 
can  be  given.  The  value  of  such  a  plant  may  be  considered  in  a 


672  Cost,  Value  and  Sale  of  Power. 

variety  of  ways:  First:  Its  value  if  intelligently  and  recently  de- 
signed, may  be  represented  by  the  cost  of  its  reproduction  plus  a 
certain  value  for  the  water  power  rights;  Second.  Its  value  may 
be  computed  on  the  capitalized  net  income  that  the  plant  can  or 
does  earn;  or,  Third:  The  value  of  the  plant  may  be  considered 
equal  to  the  capitalized  value  of  the  most  economical  plant  that 
can  be  installed  to  furnish  power  at  the  point  at  which  the  power  is 
to  be  used.  By  the  term  "most  economical"  is  meant  not  neces- 
sarily the  one  lowest  in  first  cost,  but  the  plant  that,  when  consid- 
ered in  the  broadest  sense,  will  furnish  power,  all  things  consid- 
ered, at  a  less  cost  than  from  any  other  source  of  power.  The  sub- 
ject is  a  very  broad  one  and  one  that  needs  careful  consideration 
and  study.  A  number  of  references  are  given  to  discussions  of 
this  subject  before  various  engineering  societies,  to  which  the  en- 
gineer is  referred  for  further  information  on  this  important  sub- 
ject. 


LITERATURE. 

COST   AND   VALUE   OF   WATER   POWER. 

1.  Kimball,    Geo.    A.     Water   Power:    Its    Measurement   and   Value.     Jour. 

Asso.  Eng.  Soc.  1893. 

2.  Main,  C.  T.     The  Value  of  Water  Power.    Trans.  Am.  Soc.  Mech.  Eng. 

Vol.  13,  p.  140.     Eng.  Rec.    Vol.  50,  p.  694. 

3.  Grant,  W.  H.     Calculation  of  Mean  Horse  Power  of  a  Variable  Stream. 

Trans.  Am.  Soc.  C.  E.    Vol.  22,  p.  389. 

4.  Rockwood,  G.  I.     On  the  Value  of  a  Horse  Power.     Trans.  Am.  Soc.  M.  E. 

Vol.  21,  p.  590. 

5.  Nagle,  A.  F.    An  Analysis  of  the  Commercial  Value  of  Water   Power, 

per   Horse   Power  per  Annum.     Trans.   Am.   Soc.   M.   E.     1902. 
Eng.  News,  vol.  49,  p.  83. 

6.  Parker,  M.  S.    Cost  of  Steam  and  Water  Power  in  Montana.     Jour.  Asso. 

Eng.  Soc.     Vol.  15,  p.  26. 

7.  Main,  C.  T.     Cost  of  Steam  and  Water  Power.     Trans.  Am.  Soc.  M.  E. 

Vol.  11,  p.  108. 

8.  Manning,  C.  H.     Comparative  Cost  of  Steam  and  Water  Power.     Trans. 

Am.  Soc.  M.  E.     Vol.  10,  p.  499. 

9.  Weber,  Samuel.     The  Cost  of  Water  Power.     Cassier's  Magazine,  vol.  8, 

p.  415. 

10.  Walbank,   W.    M.     Lachine    Rapids    Plant    and    the    Cost    of   Producing 

Power  Therefrom.    West.  Elec.     July  9,  1898. 

11.  Cost  of  Niagara  Power  in  Buffalo.     Elec.  World,  April  23,  1898. 


Literature.  673 

COST  OF  POWER. 

12.  Jones,  C.  L.     Electrical  World,  Feb.  18,  1905. 

13.  Emery,  C,  E.     Cost  of  Steam  Power.     Am.  Inst.  Elec.  Eng.     1895.     Trans. 

Am.   Soc.  C.   E.     Vol.  12,  p.  425.     Trans.  Am.   Inst.  Elec.  Eng. 
Vol.  10,  p.  119.     Eng.  Mag.     Vol.  8,  p.  796.     Power,  1895. 

14.  Dean,  F.  W.     Reduction  in  Cost  of  Steam  Power  from  1870  to  1897.     Am. 

Soc.  M.  E.     Vol.  9,  p.  301.     Eng.  News.     Dec.  1897. 

15.  Arnold,  B.  J.     Cost  of  Producing  Electrical  Energy.     Power,  Dec.  1894. 

16.  Gray,  C.  C.     An  Investigation  of  the  Cost  of  Power.     The  Engineer,  1902. 

Vol.  39,  p.  64. 

17.  Perry,  N.  W.     Comparative  Cost  of  Generating  Electrical  Power.     Elec. 

World,  vol.  25,  p.  274. 

18.  Rice,  C.  W.     Analysis  of  the  Cost  of  the  Generation  and  Distribution  of 

a  Unit  of  Electricity.     West.  Elec.     June  25,  1898. 

19.  Dreyfus,  E.  D.     Method  of  Investigating  the  Cost  of  Producing  Electrical 

Energy.     Electrical  World,  vol.  52,  p.  19. 

20.  Archibald,  -E.  M.     The  Effect  of  Load  Factor  on  Cost  of  Power.     Elec- 

trical Age.     Nov.  1906. 

21.  Forest,  H.  V.     Cost  of  Electrical  Power  in  Small  Central  Stations.     Elec- 

trical World,  vol.  48,  p.  1246. 

22.  Economy  of  Electric  Stations.     Report  of  Committee  on  Data  of  the  Na- 

tional   Electric   Light   Asso.     Eng.    Rec.     Vol.    36,    p.    74.     Elec. 
Eng.     Vol.  21,  p.  522. 

23.  Elecricity — Costs  and  Revenues.     Power,  May,  1903. 

24.  What  Does  a  Steam  Power  Cost?    The  American  Engineer,  1890. 

THE    SALE    OF   POWEB. 

25.  Harvey,  G.  A.     Contracting  for  Use  of  Hydro-Electric  Power  on  Railway 

Systems.     Electrical  Age,  Sept.  1906. 

26.  Storer,  S.  B.     The  Sale  and  Measurement  of  Electrical  Power.     Electri- 

cal World,  vol.  47,  p.  669.     Electrical  Age,  Aug.  1906.     Engineering 
Record,  Nov.  3,  1906. 

27.  Parsons,  C.  E.     Sale  of  Water  Power  from  the  Power  Company's  Point  of 

View.     Engineering  Record,  vol.  54,  p.  161. 

28.  The  Principles  of  Modern  Rate  Making  for  Electric  Light  and  Power. 

Electrical  World,  vol.  49,  p.  1086. 

29.  Fowler,   C.   P.     Some   Fundamental   Principles   Underlying   the   Sale   of 

Electrical  Energy.     Electrical  World,  vol.  50,  p.  456. 

30.  Burnett,  H.  R.     The  Costs  of  Electricity,  Supply,  and  Their  Relation  to 

Scale  of  Charges.     Electrical  Review,  vol.  51,  p.  172. 

POWEB  TBANSMISSION. 

31.  Donaldson,  Wm.     Transmission  of  Power  by  Fluid  Pressura     E.  &  F.  N. 

Spon,  London,  1888. 

32.  Unwin,  W.  C.     On  the  Development  and  Transmission  of  Power.     Long- 

man, Green  &  Co.,  London,  1894. 

33.  Kern,  E.  W.     Power  and  Power  Transmission.     John  Wiley  &  Son,  New 

York,  1902. 
41 


674  Cost,  Value  and  Sale  of  Power. 

34.  Mead,  Daniel  W.     Commercial  Transformation  of  Energy.     111.  Soc.  Eng. 

&  Sur.  1901.     Vol.  14,  p.  38. 

DEPKECIATION. 

35.  Matheson,   Ewing.    The   Depreciation   of  Factories.     E.   &   F.   N.    Spon. 

London,  1903. 

36.  Mogerisen,  Peter.    A  table  for  Depreciation  or  Sinking  Fun*d  Payments 

with  Annual  Compounding.     Eng.  News,  vol.  53,  p.  226. 

37.  Alvord,  J.  W.     Depreciation  Proceedings.     Am.  W.  W.  Asso.     1903. 

38.  Bolton,   R.   P.     Depreciation,   Maintenance   and   Interest   Charges.     Eng. 

Review.     Jan.  1902. 

39.  Brayan,  W.  H.     The  Appraisal  and  Depreciation  of  Water  Works.     Jour. 

Asso.  Eng.  Soc.     Dec.  1907. 

40.  Depreciation   of   Electrical   Apparatus.     Elec.   World  and   Eng.     Aug.    9, 

1902.     Iowa  Engineer.     July,   1902. 


CHAPTER  XXVIII. 

THE  INVESTIGATION   OF  WATER  POWER  PROJECTS. 

336.  The  Extent  of  the  Investigation. — The  investigation  of  any 
water  power  project  should  include  a  careful  study  of  all  available 
data  relating  to  the  physical  and  meteorological  factors  that  affect 
the   water   supply  and  that  obtain  on  the   drainage  area   of  the 
stream  on  which  the  water  power  development  is  projected.     The 
present  condition  of  these  factors  is  readily  obtainable  by  careful 
observations  and  surveys  but  the  most  difficult  and  yet  the  most 
important  information  needed  for  the  correct  understanding  of  the 
project  is  the  variations  from  present  conditions  that  have  occurred 
in  the  past  and  that  are  therefore  liable  to  re-occur  in  the  future. 
On  the  correct  interpretation  of  the  available  data  the  success  of 
the  project  or  at  least  the  economy  of  the  installation  depends,  es- 
pecially if,  as  is  usually  the  case,  it  is  desired  to  develop  the  plant 
to  its  economical  maximum. 

The  extent  of  the  investigation  must  be  governed  by  the  import- 
ance of  the  project,  and  will  also  depend  on  whether  the  investiga- 
tion and  report  are  to  be  of  a  preliminary  character,  or  are  to  be 
the  basis  of  a  final  report  on  which  the  feasibility  of  the  project 
may  be  decided. 

337.  Preliminary  Investigation  and  Report. — An  examination  of 
the  data  available  in  any  first  class  engineering  library  will  gener- 
ally give  the  information  necessary  to  form  an  approximate  judg- 
ment of  the  probable  feasibility  of  the  project  in  so  far  as  it  depends 
on  the  flow  of  the  stream.     The  approximate  area  drained  by  the 
stream  can  be  determined  by  reference  to  such  maps  as  may  be 
available  and  the  probable  flow  and  the  variations  in  the  same  that 
will  occur  from  day  to  day  and  from  month  to  month,  can  usually  be 
determined  by  the  construction  of  comparative  hydrographs  made 
from  either  the  measured  flow  of  the  stream,  if  such  information  is 
available,  .(see  Literature  page  194)  or  otherwise  on  the  compara- 
tive flow  of  similar  and  adjacent  streams  as  described  in  Sec.  51, 
page  83,  and  Sec.  100,  page  184. 


676  The  Investigation  of  Water  Power  Projects. 

From  such  an  investigation  together  with  an  appropriate  knowl- 
edge of  the  available  head,  an  estimate  of  the  probable  power  of  the 
stream  can  be  made,  and  from  such  information  an  opinion  can  be 
formed  as  to  whether  it  is  desirable  to  carry  the  investigation  fur- 
ther. Frequently  such  an  investigation  will  show  beyond  question 
the  futility  of  the  project,  and  even  an  examination  of  the  locality 
becomes  unnecessary.  If  the  preliminary  investigation  shows  that 
sufficient  power  is  probably  available  on  the  stream  in  question  the 
investigation  can  be  carried  into  sufficient  detail  to  warrant  an 
opinion  as  to  whether  or  not  the  project  is  feasable  in  all  of  its 
phases. 

338.  Study  of  Run-off. — The  information  of  primary  importance 
in  a  water  power  project  is  the  amount  and  variation  in  the  run- 
off of  the  stream  itself.  If  this  is  not  available  the  run-off  of  neigh- 
boring streams  that  have  similar  physical  and  meteorological  condi- 
tions prevailing  on  their  drainage  area  is  next  in  importance. 

As  already  pointed  out,  (see  Sec.  99,  page  181),  the  hydrograph  of 
the  actual  flow  of  the  stream  itself  is  the  best  information  for  study- 
ing its  variations  in  flow.  Such  hydrographs  must  be  available  for 
a  considerable  term  of  years,  and  it  is  desirable  that  they  should 
cover  all  extremes  of  rain-fall  and  drought,  and  other  physical  and 
meteorological  conditions  that  influence  run-off. 

In  the  investigation  of  the  hydrographical  condition  of  any 
stream,  a  single  gauging  of  the  stream  is  of  little  or  no  value.  It  is 
however,  desirabble  to  establish  a  guaging  station  as  early  as  possi- 
ble and  to  take  daily  gauge  readings.  It  is  also  important,  both  for 
the  purpose  of  an  understanding  of  the  guage  reading  and  for  the 
purpose  of  the  study  of  head,  to  make  stream  flow  measurements 
(see  Chap.  XI)  under  all  large  variations  in  flow,  as  early  as  possi- 
ble in  order  that  a  rating  curve  may  be  established. 

When  no  local  hydrographs  are  available,  or  when  such  available 
hydrographs  are  limited  to  a  few  years,  it  becomes  desirable  to 
gather  together  the  flow  data  of  all  adjacent  and  similar  streams  and 
to  construct  comparative  hydrographs  therefrom,  as  described  in 
Sec.  100,  page  184.  A  long  continued  series  of  hydrographs  of  a 
neighboring  stream  where  similar  conditions  prevail  is  important 
and  should  usually  be  utilized  even  if  local  observations  have  been 
made  for  a  few  years.  The  value  of  comparative  hydrographs  is 
dependent  on  the  similarity  of  conditions,  a  question  that  demands 
careful  consideration  and  a  considerable  amount  of  data  to  deter- 
mine, and  even  then  can  be  regarded  only  as  indicative.  It  is  also 


Study  of  Rain-Fall.  677 

essential  to  make  careful  comparisons  of  the  relations  that  exist 
between  the  hydrograph  of  the  river  under  discussion  and  those  of 
adjoining  rivers,  for  such  period  as  such  date  may  be  mutually 
available  on  both  streams,  in  order  that  variations  between  the 
areas  compared  may  be  determined. 

339.  Study   of   Rain-Fall. — The    rainfall    records    of   the   United 
States  Weather  Bureau  and,  previous  to  these,  the  records  of  the 
observations  of  the  United  States  Signal  Service   (see  Literature, 
page  130)  are  available  from  various  stations  throughout  the  United 
States  for  a  long  term  of  years.    It  is  desirable  to  collect  the  rain- 
fall data  for  the  drainage  area  of  the  stream  under  consideration, 
and  also  on  such  other  drainage  areas  as  may  be  used  for  compara- 
tive purposes.     This  information  should  be  classified  and  studied 
as  outlined  in  Chapter  VI.     In  investigating  rain-fall  it  is  usually 
especially  desirable  to  make  a  study  of  both  the  annual  rain-fall  and 
the  periodical  rain-fall  of  the  divisions  of  the  water  year.     (See  Sec. 
77,  page   126.)     The  distribution  of  the  rain-fall  of  these  periods 
has  a  greater  effect  on  the  low  water  flow  than  the  total  rain-fall 
for  the  year. 

The  relations  between  rain-fall  and  run-off  for  the  period  for 
which  complete  data  is  available  should  be  investigated  and  such 
relations  established  as  clearly  as  possible  for  the  drainage  areas 
under  conideration.  .(See  Chapter  VIII.)  With  the  information 
concerning  run-off  commonly  available  and  the  rainfall  records  for 
a  considerable  term  of  years,  it  will  be  possible  to  draw  fairly  accu- 
rate conclusions  as  to  the  probable  variation  and  average  flow  of 
the  stream.  The  probability  of  a  larger  maximum  or  a  smaller  min- 
imum than  the  stream  flow  observations  themselves  indicate  can 
also  be  determined  from  such  an  investigation. 

340.  Study  of  Topographical  and   Geological   Conditions. — The 
topographical  and  geological  conditions  may  ordinarily  be  inves- 
tigated from  data  available  in  the  publications  of  the  United  States 
Geological   Survey,  or  of  the  Geological   Surveys  of  the  state  in 
which  the  drainage  area  may  lie.    The  information  sought  from  this 
investigation  is  a  knowledge  of  the  conditions  that  will  effect  run- 
off, consequently,  such  a  study  is  not  of  particular  importance  pro- 
vided sufficient  rain-fall  and  run-off  data  is  available  for  the  purpose 
of  the  investigation. 

If.  however,  the  hydrographical  condition  o'f  the  areas  under 
consideration,  or  of  other  adjacent  and  similarly  located  areas  have 
not  been  previously  investigated,  and  if  few  or  no  local  observa- 


678  The  Investigation  of  Water  Power  Projects. 

tions  of  stream  flow  have  been  made,  the  topographical  and  geolog- 
ical data  may  form  the  basis  of  a  more  intelligent  opinion  in  regard 
to  the  probable  run-off  than  can  be  obtained  without  such  considera- 
tion. In  any  event,  this  source  of  information  should  be  utilized  to 
the  full  extent  warranted,  as  should  all  other  sources  of  information 
that  will  in  any  way  assist  the  engineer  in  an  intelligent  understand- 
ing of  the  problem  before  him,  and  the  formation  of  a  correct  opin- 
ion as  to  the  possibilities  and  probabilities  of  the  case  in  question. 

341.  Study  of  Flood-Flow. — It  is  important  to*  establish  both  from 
information  that  is  usually  available  in  the  stream  valley  under  con- 
sideration, and   from   information   which   may   be   available   from 
adjoining  streams,  the  probable  maximum  flood-flow  of  the  stream. 
This  must  be  determined,  or  at  least  a  safe  approximate  estimate 
must  be  made  in  order  that  the  dam  and  other  works  for  the  control 
of  the  flow  can  be  intelligently  designed.     (See  Sec.  93,  page  163.) 

After  the  rating  curve  has  been  established  the  elevation  of  the 
high  water  marks  in  the  immediate  vicinity  and  the  relation  of  the 
same  to  guage  heights  will  usually  give  a  safe  basis  for  the  estimate 
of  extreme  flood-flows. 

342.  Study  of  the  Back-Water  Curve. — A  topographical  survey 
of  the  proposed  site  of  the  dam  and  of  the  stream  valley  above  the 
dam  site,  to  the  probable  practical  limit  of  the  back-water  effect, 
should  be  carefully  made.     In  order  to   investigate   the   probable 
height  of  the  back-water  under  all  conditions  of  flow  it  will  be  neces- 
sary to  make  cross-sections  of  the  river  at  such  intervals  and  under 
such   conditions  as  will  permit  of  the   division  of  the  river  into 
lengths  or  divisions  having  comparatively  uniform  sections.    Gages 
should  then  be  established  at  the  various  stations  and  observations 
should  be  made  of  the  gage  heights  at  each  station  during  various 
stages  of  flow  (see  Chapter  X).      From  the  quantity  of  water  flow- 
ing at  any  stage,  together  with  the  cross  sections  of  the  river  on  the 
various  divisions,  the  value  of  the  hydraulic  elements  and  especially 
of  the  friction  coefficients  for  each  division  and  their  variations  un- 
der such  condition  of  flow,  can  be  calculated.      (See  Sees.  37  to  40, 
page  44.)     After  this  has  been  do<ne  it  is  possible  to  calculate  the 
back-water  curve  (see  Sec.  42,  page  58)  and  to  establish  the  prob- 
able limit  of  the  back-water  flow  line  under  any  other  conditions  of 
flow  in  a  fairly  reliable  manner. 

.Study  of  Head. — The  consideration  of  these  conditions,  the  height 
of  the  water  surface  at  the  dam  due  to  various  sections  and  length 
of  the  spill-way  and  the  practicable  limit  to  which  flood  height  in 


Study  of  Storage  and  Pondage.  679 

the  valley  above  must  be  restricted,  will  usually  establish  the  limit 
of  the  height  to  which  the  dam  can  or  should  be  built  and  will  in- 
dicate whether  it  is  necessary  or  desirable  to  construct  flood  gates 
or  to  use  an  adjustable  crest,  flash  boards,  or  means  for  regulating 
and  limiting  the  flood  height.  When  these  conditions  are  estab- 
lished the  variations  in  head  under  various  conditions  of  flow  can 
be  determined  (see  Chap.  V,  page  93)  and  the  effect  of  such  varia- 
tions on  the  power  which  may  be  developed  can  be  calculated.  (See 
Sec.  62,  page  103.) 

343.  Study  of  Storage  and  Pondage. — The  topographical  survey 
will  also  give  information  concerning  the  storage  and  pondage  con- 
dition immediately  above  the  dam.    In  special  cases,  reservoirs  be- 
yond the  limit  of  the  back-water  effect  may  be  desirable  and  special 
surveys  under  such  conditions  will  be  necessary.    As  the  conditions 
of  pondage  and  storage  materially  effect  the  amount  of  power  avail- 
able, these  questions  frequently  become  of  great  importance  and 
should  receive  the  attention  of  the  engineer  that  their  importance  in 
each  particular  case  seems  to  warrant.    After  definite  information  is 
obtained  concerning  the  extreme  permissible  limit  of  flood-flow,  and 
the  possibilities  of  storage  and  pondage,  an  estimate  of  the  power 
of  the  stream  under  various  conditions  of  use  can  be  readily  matfe. 
(See  Chap.  XXVI.) 

344.  Study  of  Probable  Load  Curve. — It  is  important  in  consider- 
ing the  power  of  the  stream  and  especially  the  desirable  condition 
of  pondage,  to  ascertain  as  far  as  practicable  the  probable  necessary 
distribution  of  the  demand  for  power  throughout  the  day.    The  way 
in  which  the  power  is  to  be  used,  whether  on  10  hour,  12  hour,  or 
24  hour  service,  and  its  probable  variation  during  the  hours  of  use, 
has  a  most  important  bearing  on  the  design  of  the  plant.     (See  Chap- 
ters  XVII  and   XXI.)      If  variations   in  the   demand   for  power 
throughout  the  year  are  also  likely  to  occur,  and  such  variations  are 
likely  to  effect  the  requirements  for  storage,  they  must  also  receive 
consideration. 

A  census  of  the  power  used  in  the  district,  to  be  supplied  from  the 
proposed  water  power  development,  is  important  and  should  be 
made  in  as  great  detail  and  with  as  great  care  as  practicable.  An 
accurate  estimate  of  the  amount  of  power  used  by  a  factory  or  man- 
ufacturing plant  is  a  matter  of  considerable  difficulty.  In  some 
plants  where  power  is  electrically  distributed,  the  use  of  indicating, 
and  sometimes  of  recording  instruments,  make  it  very  easy  to  deter- 
mine the  energy  output  of  the  power  plant.  In  most  manufacturing 


680  The  Investigation  of  Water  Power  Projects. 

establishments  where  power  is  distributed  by  belts,  shafting,  and 
other  than  electrical  means,  the  amount  of  power  actually  developed 
and  utilized  is  seldom  definitely  known.  The  use  of  the  steam  engine 
indicator,  if  opportunity  for  such  use  is  offered,  will  give  a  knowl- 
edge of  the  indicated  power  of  the  engine  at  the  time  observations 
are  made;  and  if  the  probable  variations  are  investigated,  a  fairly 
close  estimate  of  power  used  can  often  be  made  by  this  means. 

The  annual  quantity  of  coal  used,  and  a  careful  study  of  the  con- 
dition and  character  of  the  boiler  service,  requirements  for  heating, 
condition  of  the  engine  used,  together  with  a  careful  examination 
of  the  machinery  operated,  will  form  the  basis  of  a  fairly  approxi- 
mate estimate  of  power  used.  Even  where  the  estimate  of  power 
used  is  fairly  accurate,  it  must  be  remembered  that  when  such 
power  is  used  and  transmitted  through  a  multitude  of  shafts,  belts, 
etc.,  that  if  the  electric  power  is  substituted  and  individual  motors 
used  on  the  machine  to  be  operated,  the  power  then  used  will  be 
Tery  greatly  reduced  in  amount. 

345.  Study    of    Power    Development. — Having    established    the 
probable  load  curve,  the  head  under  all  conditions  of  flow,  and  the 
flow  as  modified  by  the  pondage  or  storage  conditions,  the  extent  of 
the  power  development  can  be  determined.    All  of  the  questions  that 
have  been  previously  discussed  lead  up  to  the  consideration  of  the 
question  of  the  desirable  capacity  or  extent  of  the  proposed  power 
development.     This  capacity  should  always  be  estimated  on  a  con- 
servative basis.     If,  as  is  usually  the  case,  uncertainties  exist  as  to 
the  probable  demand  and  distribution  of  power,  or  the  probable  min- 
imum flow  of  the  stream,  it  is  desirable  to  develop  the  project  to  a 
point  below  the  probable  commercial  maximum  but  to  keep  in  mind 
the  probability  of  the  desirability  of  future  enlargements  and  to 
consider  the  plans  with  the  future  in  view.     In  this  connection  the 
question  of  auxiliary  power,  and  the  capacity  of  the  plant  as  modi- 
fied by  such  power,  should  receive  attention. 

346.  Study  of  Auxiliary  Power. — The  necessity  of  auxiliary  power 
in  connection  with  the  proposed  water  power  development  can  be 
determined  by  an  intelligent  study  of  the  hydrograph  and  an  inves- 
tigation of  the  effects  thereon  of  the  storage  and  pondage  available. 
(See  Sec.  317.)     As  a  general  principle,  it  may  be  stated  that  a 
stream  can  often  be  developed  to  commercial  advantage  to  the  ex- 
tent of  the  power  which  will  be  uniformily  available  for  eight  or 
nine  months  of  the  dryest  year,  and  that  auxiliary  power  is  usually 
warranted  to  furnish  the  power  needed  for  the  remainder  of  the  sea- 


Study  of  Plant  Design.  68 1 

son.  This  is  a  general  rule  which  must  be  applied  with  caution. 
Every  proposed  development  must  be  carefully  investigated  for  it- 
self, and  no  general  conclusion  should  form  the  basis  of  a  final  re- 
port on  the  feasibility  of  such  a  project.  The  greater  the  demand 
for  power,  and  the  greater  the  cost,  of  development  from  other  than 
water  power  sources,  the  more  expense  is  warranted  for  auxiliary 
service,  pondage,  etc.,  and  the  greater  the  capacity  to  which  the 
water  power  should  be  ultimately  developed. 

347.  Study  of  Site  of  Dam  and  Power  Station. — In  addition  to 
the  topographical  survey  previously  mentioned,  it  is  necessary  to 
examine  in  considerable  detail  the  bed  and  banks  of  the  stream  and 
make  all  necessary  soundings  to  fully  establish  all  conditions  on 
which  the  character  of  the  construction  recommended  must  depend. 
It  is  important  that  all  conditions  be  carefully  investigated  and  the 
type  of  construction  to  be  recommended  carefully  considered.    The 
storage  of  energy  almost  always  involves  a  hazard  which  must  be 
met  with  economical  but  safe  design  and  construction.    The  preven- 
tion of  flow  under  and  around  the   structure  requires  a  detailed 
knowledge  of  the  local  conditions  and  is  one  of  the  most  uncertain 
conditions  which,  unless  carefully  and  correctly  estimated,  is  apt 
to  result  in  considerable  extra  expense.    The  flood  flow  is  a  condi- 
tion which  needs  the  most  careful  consideration  for  it  is  often  the 
condition  of  greatest  danger  and,  to  assure  safe  construction  during 
the  short  period  when  such  conditions  obtain,  requires  special  atten- 
tion and  intimate  knowledge  of  the  local  conditions,  and  often  in- 
volves considerable  expense. 

348.  Study  of  Plant  Design. — The  study  of  plant  design  requires 
an  extensive  study  of  the  various  types  of  development  that  are  in 
practical  use  and  the  adaptability  of  such  designs  to  the  conditions 
of  the  particular  locality  under  consideration.     It  is  seldoim  that 
plans,  no  matter  how  successfully  carried  out  in  one  place,  can  be 
duplicated  to  advantage  in  another.     Each  plant  should  be  built  to 
meet  the  particular  conditions  under  which  it  is  to  be  installed  and 
operated,  and  the  best  ideas  from  all  sources  that  will  apply  to  the 
local  conditions  should  be  correlated  and  embodied  in  the  proposed 
plant.   Extensive  experience,  observation,  and  study  are  each  desir- 
able and  each  essential  for  the  best  results.      For  his  own,  as  well  as 
for  his  client's  good,  the  engineer  should  endeavor  to  secure  the  very 
best  results  possible  when  all  things  are  carefully  weighed  and  con- 
sidered.   No  reasonable  amount  of  conscientious  work,  painstaking 
thought,  study,  labor  or  expense  should  stand  in  the  wav  of  such 


682  The  Investigation  of  Water  Power  Projects. 

results;  and  anything  less  than  this  is  a  detriment  to  future  pro- 
fessional attainments  which  no  engineer,  young  or  old,  can  afford. 

In  the  previous  chapters  the  general  principles  underlying  the 
design  of  the  various  elements  of  the  plant  have  been  considered. 
The  consideration  of  these  matters  has  been  very  brief  and  the  en- 
gineer must  extend  his  study  in  all  cases  to  the  extensive  literature 
on  each  subject,  reference  to  some  of  which  has  been  given  at  the 
end  of  most  chapters.  Additional  references  can  be  found  in  the  En- 
gineering Index  and  in  the  indexes  to  the  various  technical  publica- 
tions and  the  publications  of  the  various  engineering  societies.  A 
personal  visit  to  and  a  detailed  examination  of  successful  plants  is 
a  method  for  the  acquisition  of  exact  knowledge  which  should  not 
be  neglected.  New  novel  and  untried  designs  are  frequently  de- 
scribed in  engineering  publications.  If  they  are  successful  their  suc- 
cess is  often  heralded  in  a  similar  manner.  Their  failure  is  seldom 
mentioned  by  the  technical  press  and  the  only  method  of  ascertain- 
ing their  true  value  is  by  personal  and  confidential  inquiry  on  the 
ground. 

349.  The  Estimate  of  Cost. — In  order  that  the  preliminary  esti- 
mate shall  be  made  on  a  safe  basis,  reasonable  allowances  should  be 
made  for  unforeseen  and  possible  contingencies.  This  is  especially 
desirable  in  preliminary  estimates  on  which  the  feasibility  of  the  en- 
tire project  may  be  based.  If  a  safe  estimate  of  the  actual  cost  of 
construction, — that  is  an  estimate  which  will  surely  not  be  exceeded 
and  will  undoubtedly  be  reduced  in  construction, — makes  the  feasi- 
bility of  the  project  doubtful,  then,  as  a  general  proposition,  the 
project  is  not  worthy  of  further  consideration.  If  the  project  is 
predicated  on  the  basis  of  an  estimate  that  is  known  to  be  safe,  it 
can  lead  to  no  unfortunate  investments.  The  owners  of  a  develop- 
ment are  always  satisfied  if  the  cost  of  development  is  less  than  the 
engineer's  estimate ;  but  an  increase  in  cost  is  often  a  serious  matter. 

The  desire  to  develop  a  project  is  sometimes  apt  to  give  an  opti- 
mistic coloring  to  the  engineer's  report.  This  is  a  tendency  which, 
both  on  account  of  the  interest  of  his  client  and  his  own  future  repu- 
tation, he  should  carefuly  guard  against. 

If  the  feasibility  of  the  project  is  reasonably  well  established  by 
the  preliminary  examination,  the  examination  should  be  still  further 
extended  and  made  fairly  complete.  Preliminary  plans  should  be 
outlined  in  order  that  a  safe  detailed' estimate  may  be  made.  The 
expense  involved  in  such  preliminary  work  is  well  warranted  by  the 
results  obtained.  In  many  cases  plants  have  been  recommended  on 


The  Report.  683 

insufficient  examination,  and  the  estimates  made  with  too  optimistic 
a  view  of  the  conditions  to  be  met.  The  latter  development  of  the 
necessity  of  increased  expense,  has  made  the  project  less  attractive 
and  has  resulted  in  great  disappointment  both  to  the  owners  and  to 
the  engineer  on  whose  opinion  the  work  has  gone  forward. 

350.  The  Report. — As  far  as  practicable  the  engineer,  in  making 
a  report  on  a  water  power  project,  should  furnish  his  client  with  all 
of  the  data  on  which  his  ^deductions  are  based.  He  should  discuss 
this  data  and  its  bearing  on  the  project  and  point  out  as  clearly 
as  possible  the  reason  for  the  opinions  he  expresses.  In  a  well' 
drawn  report  the  engineer  can  usually  so  illustrate  and  describe  the 
conditions  by  which  a  project  is  modified  and  controlled,  that  any 
good  business  man  will  understand  the  basis  on  which  his  opinion 
rests  and  the  degree  of  probability  of  any  departure  from  the  ex- 
pected result.  While  this  is  not  true  in  regard  to  the  technical  de- 
tails, it  is  entirely  true  with  the  general  consideration  on  which  the 
feasibility  of  a  project  rests.  If  a  report  can  not  be  so  drawn  it  is 
due  either  to  insufficient  data  or  to  the  fact  that  the  engineer  him- 
self does  not  fully  understand  and  appreciate  the  logic  of  the  situa- 
tion. 

In  general,  a  complete  report  on  a  water  power  project  should 
include  a  careful  consideration  and  discussion  of  the  following: 

First :  A  general  description  of  the  drainage  area,  including  the 
size  and  the  topographical,  geological,  and  other  physical  conditions 
that  may  have  a  direct  bearing  on  the  feasibility  of  the  project. 

Second :  The  run-off  data  available  on  the  streams  in  question,  if 
any  such  data  exists. 

Third:  If  local  run-off  data  is  available,  but  only  for  a  brief  term 
of  years,  the  rainfall  of  the  district  for  as  long  a  period  as  possible 
should  be  collected,  and  its  relations  to  the  available  run-off  data 
established.  From  this  the  probable  modification  of  the  run-off 
during  other  years  during  which  the  rainfall  is  found  to  vary,  should 
be  carefully  and  fully  discussed. 

Fourth :  The  run-off  data  on  adjoining  streams,  having  drainage 
areas  with  similar  physical,  topographical  and  geological  condi- 
tions, and  where  the  hydrographical  conditions  of  the  rainfall  and 
run-off  are  apparently  similar,  when  the  difference  therein  can  be 
determined  and  estimated,  should  be  graphically  presented  and  dis- 
cussed. 

Fifth :  The  relations  of  the  rainfall  and  of  other  conditions  on  the 


•684  The  Investigation  of  Water  Power  Projects. 

comparative  areas  considered,  and  their  variations  from  the  par- 
ticular location  tinder  consideration,  should  be  fully  illustrated. 

Sixth :  The  conclusion  in  regard  to  the  probable  flow  from  the 
drainage  area,  considered  on  the  basis  of  its  run-off,  and  the  run-off 
of  comparative  areas  should  be  fully  considered. 

Seventh :  A  general  description  of  the  locality  at  which  the  dam 
and  power  stations  are  to  be  constructed,  and  the  physical  condi- 
tions there  existing,  also  the  effect  of  such  conditions  upon  the  con- 
struction of  the  plant,  should  be  described  and  the  methods  of  meet- 
ing them  should  be  carefully  and  fully  outlined. 

Eighth :  The  head  available  and  the  variations  under  various  con- 
ditions of  flow  should  receive  careful  consideration. 

Ninth :  The  probable  power  available  with  and  without  pondage, 
or  with  the  pondage  found  by  the  preliminary  survey  to  be  avail- 
able, should  be  carefully  and  fully  treated,  as  this  is  one  of  the  essen- 
tial features  of  the  report. 

Tenth :  The  auxiliary  power,  if  any,  necessary  to  maintain  the 
plant  at  all  times  to  the  capacity  recommended,  often  needs  specific 
discussion. 

Eleventh :  An  estimate  should  be  made  of  the  probable  cost  of  the 
development,  the  probable  operating  expenses,  and  the  probable 
cost  of  maintenance. 

Twelfth :  The  probable  market  for  the  power  to  be  generated,  and 
the  probable  distribution  of  the  demand  for  the  power  through  the 
day  and  year,  and  the  basis  on  which  such  estimates  are  made, 
should  be  given. 

Thirteenth :  The  sources  of  power  used  in  the  territory  which  it  is 
proposed  to  supply,  the  cost  of  developing  the  same,  and  the  prob- 
able price  at  which  power  can  be  sold,  are  of  primary  importance. 

Fourteenth :  The  report  should  be  accompanied  by  hydrographs, 
preliminary  plans,  and  such  other  drawings  as  will,  with  the  data 
furnished,  show  conclusively  that  the  facts  are  as  the  report  sets 
forth. 

Fifteenth :  In  general  it  is  advisable  that  the  report  itself  should 
be  clear,  concise  and  definite  in  its  statements  and  recommenda- 
tions. Any  elaborate  discussion  of  voluminous  data  should  be  fur- 
nished in  the  form  of  an  appendix  to  which  the  main  report  should 
refer  for  confirmation  of  its  findings  and  recommendations. 


APPENDIX—  A. 

WATER  HAMMER. 

In  Chapter  XVIII,  Section  213,  it  is  shown  that  the  pressure  head 
due  to  a  change  of  velocity  in  a  water  column  is  expressed  by  the 
formula 


It  is  evident  that  the  water  hammer  head  produced  by  the  rapid 
closing  of  a  gate  at  the  end  of  a  pipe  line  will  be  maximum  for  the 

dv 
maximum  possible  value  of-j—  >  or  that  obtained  by  closing  the  gate 

instantly.  Were  it  not  for  the  elasticity  of  water  and  pipe,  instan- 
taneous gate  closure  would  produce  an  infinite  rate  of  retardation, 

dv 

-fa>   and  hence  infinite  pressure.      In  reality  the  water  near  the  gate 

first  compresses  and  the  surrounding  pipe  expands,  due  to  the  water 
hammer  pressure,  the  flow  meanwhile  continuing  undiminished  in 
the  remainder  of  the  pipe  in  order  to  fill  the  additional  space  thus 
obtained.  The  point  up  to  which  this  compression  of  the  water  has 
taken  place,  as  shown  by  Joukowsky  *  travels  along  the  pipe  from 
gate  to  reservoir  as  a  wave  with  a  velocity,  A,f  equal  to  that  of 

*  See  the  "Memoires  of  the  Imperial  Acadainemy  of  Sciences  of  St.  Peters- 
burg," vol.  IX,  No.  5.  Ueber  den  Hydraulipchen  Stoss  in  Wasserleitungsrohren, 
by  N.  Joukowsky;  published  in  German  and  Russian.  See  also  the  synopsis 
of  same  by  O.  Simin  in  The  Trans,  of  the  American  W.  W.  Ass'n,  1904. 

t  A.  varies  from  about  4,500  to  3,000  feet  per  second  as  the  size  uf  the   pipe- 
increases,  and  can  always  be  obtained  by  the  formula  (due  to  Joukowsky)  : 

12 


_   _      _d_ 

where: 

A  =  velocity  of  the  wave  in  feet  per  second. 
K  =  volumnar    modulus    of    elasticity    of  the  water  =  294, 000s 

pounds  per  square  inch, 
e  =  thickness  of  the  pipe  walls  in  inches. 
E  =  modulus  of  elasticity  of  the  material  of  the  pipe, 
w,  g,  and  d  =  as  previously  defined  in  Chapter  XVIII. 


686  Water  Hammer. 

sound  in  the  same  column  of  water.  The  water  has  not  all  been 
brought  to  rest  until  the  wave  reaches  the  reservoir,  which  evi- 
dently requires  a  timey.  Although  only  an  elementary  length  of 
the  water  column  is  brought  to  rest  at  a  time,  the  effect  upon  the 
pressure  is  the  same  as  would  result  from  retarding  the  whole  col- 
umn as  a  unit  in  a  time^-.  The  maximum  possible  rate  of  retar- 
dation is  hence 


dv  1 

Max'  dF  =  v  -*-  T 


From  Equation  (i) 


(2)  Hm  =  maximum  ha  —  —  .  -T-  = 

The  pressure-head  given  by  this  formula  varies  from  about  140 
to  100  feet  per  foot  of  extinguished  velocity  as  the  pipe  increases 
in  size  from  2!'  upwards.  If  the  gate  is  only  partially  closed  by  this 
instantaneous  motion,  the  pressure  head  is  given  by  the  same  for- 
mula in  which  case  v  represents  the  amount  of  the  velocity  which  is 
instantaneously  extinguished. 

Thus,  in  the  case  of  instantaneous  gate  movement,  the  pressure  is 
not  produced  at  the  same  instant  along  the  entire  pipe,  but  travels 
as  a  wave  with  a  velocity  A  from  the  gate  to  the  origin  of  the  pipe 
and  back  again  to  the  gate.  It  then  reverses  and  becomes  a  wave 
of  rarefaction  which  travels  twice  the  length  of  the  pipe  in  the  same 
manner.  This  continues  until  the  energy  of  the  moving  column  of 
water  has  been  dissipated  by  friction,  and  the  wave  gradually  sub- 
sides. This  phenomenon  is  identical  with  that  of  the  vibrating 
sound  wave  in  an  organ  pipe. 

Although  equation  (2)  gives  the  maximum  possible  pressure 
head  which  can  result  from  the  extinction  of  a  given  velocity  v  in 
a  pipe  it  does  not,  however,  represent  the  maximum  pressure  which 
could  be  obtained  as  the  result  of  several  successive  gate  move- 
ments ;  in  fact,  no  limit  can  be  assigned  to  the  pressure  which  might 
result  in  case  several  water  hammer  waves  were  to  be  produced  at 
intervals  differing  approximately  by  multiples  of  the  vibration 

*  This  formula  is  the  same  as  that  obtained  by  Joukowsky  by  two  other 
methods  of  analysis.  His  discussion  of  water  hammer  phenomena  includes 
all  that  is  known  upon  the  subject  and  it,  or  Simin's  spnopsis,  should  be  read  es- 
pecially by  every  engineer  interested  in  high  head  developments  as  the  subject 
can  only  briefly  be  touched  in  this  book. 


Water  Hammer.  687 

period  of  the  water  column,  in  which  case  they  are  known  to  "pile 
up"  to  enormous  indeterminable  pressures. 

When  the  flow  in  a  pipe  is  shut  off  by  the  gradual  closure  of  a 
gate  then  equation  (i)  and  also  the  following  equation 


from  Chapter  XIX,  sections  213  and  217,  apply  as  before  except  that 
in  this  case  not  only  v  but  also  V  is  a  variable,  its  value  being  differ- 
ent for  each  successive  position  of  the  gate,  and  its  law  of  variation 
depending  upon  the  law  and  rate  of  gate  movement-  The  integra- 
tion of  equation  (3)  in  its  general  form,  to  obtain  the  velocity  curve 
is  then  very  difficult  if  not  impossible. 

An  approximate  curve  of  v,  and  hence  also  of  h  can  be  plotted  by 
assuming  the  gate  closure  to  take  place  by  means  of  a  great  many 
small  instantaneous  movements,  according  to  any  law  which  may 
be  chosen.  The  value  of.V  for  each  of  the  many  gate  positions  can 
then  be  computed  from  the  known  hydraulic  data  of  the  wheels 
and  penstock. 

Now,  in  equation  (3),  substitute  for  v  the  initial  velocity  in  the 
pipe,  and  for  V  the  normal  velocity  (above  determined),  after  the 
gate  has  received  its  first  small  instantaneous  movement.  The  re- 

dv 

suit  will  be  the  initial  slope  of  the  v-t  curve  =^r.      Assume    this 

at0 

rate  of  decrease  in  velocity  to  continue  constant  for  the  short  in- 
terval between  successive  gate  movements ;  then  the  actual  velocity, 
v,  at  the  instant  of  the  next  gate  movement  will  be 

(4)  •>..      T-T-J€ 

where  i  is  the  interval  between  the  two  movements. 

Assume  this  new  value  of  v,  to  be  v0  and  using  the  value  of  V  for 
the  corresponding  (or  second)  gate  position,  again  apply  equations 
(3)  and  (4),  until  the  gate  is  completely  shut. 

Having  thus  determined  the  v-t  curve,  the  head  curve  can  be 
readily  found  from  equation  (i),  which  gives  the  excess  of  head 
above  static  or  so  called  water  hammer  head. 

dv 
Substituting  the  value  of  — r—  from  (3)  in  (1)  gives 

(5)  ha  =  : 


Church  has  investigated  this  problem  by  a  method  described  in 
the  Journal  of  the  Franklin  Institute  for  April  and  May,  1890. 


APPENDIX-B. 

SPEED  REGULATION,  A  MORE  DETAILED  ANALYSIS 
THAN  IN  CHAPTER  XVIII. 

In  Chapter  XVIII,  Section  217,  the  following  equation  was  shown 
to  express  the  rate  of  acceleration  of  water  in  the  penstock  subse- 
quent to  an  instantaneous  change  in  gate  opening  of  the  wheel. 


dF^—V1      IT* 
Separating  the  variables  v  and  t,  gives 

dt=lvs     dv 


gH    '  V2-v2 
Integrating  we  have: 


To  determine  the  constant  of  integration,  C,  assume  that  v  —  v0 
when  t  =  0,  hence 

C  =   -  —   loge  V~VO 

Let 

(3) 


(4)  B=^ 


V-vo 
Substituting  these  values  of  C,  B  and  k  in  (2),  gives, 


From  the  definition  of  a  logarithm:    if  X  =  loge  N,  then  ex  =  N 
hence 


Solving  for  v  we  obtain: 
(7)  ^ 


Bekt4-l 


From  the  principles  of  logarithms  we  have: 

kt          **  k/t 

e      =10  *-3    =  10 


Change  of  Penstock  Velocity. 


689 


hence 


(8-) 


v  =  V 


BX  antilogk't  —  1 


'  B  X  antilog  k '  t  +  1 

Equation  (8)  is  very  readily  applied  to  finding  the  curve  of 
velocity  increase  or  decrease  in  any  pipe  line  subsequent  to  a  sudden 
change  of  gate  opening.  It  has  been  experimentally  demonstrated 


I 


L 


2  3 

TIME:  -  SECONDS 


Fig.  403.— Curve  Showing  the  Acceleration  of  Water  in  a  Pipe  Line  After 
a  Sudden  Opening  of  the  Gate. 


for  the  acceleration  of  water  in  the  drive  pipe  of  an  hydraulic  ram, 
as  shown  by  Fig.  403  which  is  taken  from  Bulletin  No.  205,  Uni- 
versity of  Wisconsin,  Engineering  Series,  Vol.  4,  No.  3,  "An  Investi- 
gation of  the  Hydraulic  Ram,"  by  the  writer. 

•  The  curve  is  the  plot  of  equation  (8)  and  the  experimental  points 
were  determined  by  an  especially  designed  instrument.     The  fact 
that  they  fall  commonly  below  the  theoretical  curve  is  due  to  a 
systematic  friction  error  in  the  instrument.    The  agreement  is  suf- 
ficiently close,  however,  to  entirely  verify  the  form  of  equation  (8). 
Fig.   404    shows    the    curves    determined    from    equation    (8)  for 
42 


690 


Speed  Regulation. 


the  wheel  used  for  illustrative  problems  in  Chap.  XVIII,  Section 
228.  Acceleration  curves  are  shown  for  changes  from  o  to  the  ve- 
locities of  %,  %>  -9  and  full  loads ;  retardation  curves  from  an  initial 
velocity  of  5'  per  sec.  to  the  above  velocities.  It  will  be  observed 
that  in  each  case  the  actual  velocity  approaches,  but  theoretically 
never  equals,  the  normal  value,  V,  for  the  given  gate  position. 

The  values  of  the  constants  used  in  computing  these  v-t  curves 
are  given  below.  B,  for  accelerating  from  an  initial  velocity  of 
zero,  is: 

V  +  v        V 


TIME    IN    SECONDS 


Fig.  404.—  Curves  of  Acceleration  and  Retardation  of  Water  in  Penstock  for 
Various  Gate  Movements. 

The  other  constants  are:  H  =  50',  1  =  500',  and  v0  =  5'  for  re- 
tardation curves  ;  also  for  the  retardation  curves  B  is  negative,  since 
v0  is  greater  than  V.  If  we  always  use  the  positive  value  of 


V  o 

we  will  obtain  two  equations: 

For  increasing  velocities  or  acceleration 

(9)  antilogk't-1 
antilog  k't  +  1 

For  decreasing  or  retarding  velocities, 

(10)  _  y  B  antilog  k't+1 

Bantilogk't-  1 


Change  of  Penstock  Velocity. 
From  equations  (3)  and  (4)  we  obtain  the  table, 


691 


Load. 

1.0 

.9 

.5 

.25 


V. 

4.77 
4.49 
2.88 
1.94 


B 

41.3 
19.1 
3.71 
2.27 


k' 

.585 

.623 

.975 

1.444 


The  computations  of  v,  by  equations  (9)  and  (10),  for  various 
assumed  values  of  t  is  very  simple  if  tabulated  as  below.  The 
computation  of  the  curve  of  acceleration  and  retardation  of  water 
in  the  penstock  from  0,  and  from  5  feet  per  second,  respectively,  to 
its  value  2.88  ft.  per  sec.  for  %  load  is  shown.  It  is  assumed  that 
the  gate  opens  instantly  from  0  to  its  position  at  %  load,  and  closes 
to  this  position  instantly  when  the  velocity  is  5'  per  sec.,  giving 
the  values  of  velocity  in  columns  v  and  v',  (4)  and  (6) ,  respectively. 

Computation  of  v-t  curve.* 
H  =  50',  1  =  500',  d  =  8',  k'  =  .975,  B  =  3.71,  v0  =  0  and  5',  V  =  2.88', 


(1) 

(2) 

(3) 

(4)  =v 

(5) 

(6X.-V1 

t 

k't 

antilog  of 
k't 

<3)-l0oo 

(3)  X3.71 

(5)  +  1  0  S8 

<3)  +  l- 

(5)-l~ 

.0 

.0 

1. 

.0 

3.71 

5.0 

.1 

.0973 

1.261 

.321 

4.64 

4.17 

o 

.1946 

1.565 

.635 

5.81 

4.077 

.4 

.3892 

2.45 

1.210 

9.10 

3.59 

.6 

.5838 

3.835 

1.690 

14.23 

3.31 

.8 

.7784 

6.003 

2.055 

22.27 

3.15 

1.0 

.973 

9.397 

2.327 

34.85 

3.05 

1.2 

1.168 

14.72 

2.513 

54.70 

2.99 

1.4 

1.362 

23.01 

2.64 

85.5 

-.95 

1.7 

1.654 

45.08 

2.753 

167.3 

2.91 

2.0 

1.946 

88.31 

2.81 

328.0 

2.897 

*  A  number  enclosed  in  parenthesis  refers  to  the  value  given  in  the  column  of 
that  number. 

Referring  again  to  Figure  404  we  see  that  the  acceleration  curves 
thus  computed  all  have  a  common  tangent  at  the  origin  showing  an 
initial  rate  of  acceleration  in  each  case  of, 

dv    _  gH 
~dtT:   ~T~ 

The  initial  rate  of  retardation,  however,  depends  upon  the  gate 
opening. 


692  Speed  Regulation. 

As  shown  by  equations  (9),  (10)  and  the  curves  in  Figure  404  the 
velocity  never  equals,  but  approaches  indefinitely  near,  to  its  normal 
value,  V,  for  a  given  gate  opening. 

To  show  the  application  of  the  foregoing  discussion  to  the  change 
of  penstock  velocity,  power,  speed,  etc.,  at  a  change  of  load,  refer  to 
Figure  405.  Here  the  line  A  B  represents  J  load,  line  C  C  repre- 
sents full  load,  line  D  D  .8  load  and  line  H  H  45  per  cent  load  for 
the  same  wheel  discussed  above.  Lines  A7  B',  C'  C'  and  D'  D' 
represent  the  corresponding  hydraulic  power  input  lines.  Line 
abccba  represents  the  line  of  gate  movement  from  its  initial  position 
at  14  to  its  position  at  full  load  and  back  again  to  %  load.  Line  O 
Cv  C  is  copied  from  Figure  (404)  and  represents  the  curve  of  velocity 
increase  which  would  result  from  a  sudden  complete  opening  of  the 
gate.  At  b  the  gate  begins  to  open,  and  the  velocity  to  increase 
along  an  estimated  curve  Bv  Cv .  This  curve  could  be  more  accu- 
rately determined  by  the  process  outlined  in  Appendix  A,  but  was 
not  so  determined  here.  In  the  same  way  curve  F  Bxv  A^  wras  taken 
from  Figure  404  and  the  velocity  curve  during  gate  movement,  C'v  B"'v. 
was  estimated. 

Having  thus  obtained  the  velocity  curve  Av  Bv  Cv  C-C'V  B'v  Av , 
the  curve  of  effective  head  at  the  wheel  can  be  readily  determined 
from  equation  (11)  Chapter  XVIII,  or 

(H)  h=^H' 

While  the  gate  is  in  motion  from  b  to  c  the  valve  of  V  changes, 
but  can  be  readily  estimated  by  interpolation  from  the  values  at 
!/4  and  full  gates.  From  c  to  c  (gate  curve)  V  is  constant,  and 
equal  to  4.77  ft.  per  second.  Since  the  friction  loss  in  the  pen- 
stock is  slight  in  the  problem  under  discussion  H'  is  assumed  to 
equal  H  =  50'.  The  resulting  curve  for  h  is  Ah  BhChCh  C'h  B'h  Ah. 

The  curve  of  hydraulic  horse  power  or  input  was  then  determined 
by  applying  the  equation  below  to  several  points  along  the  v  and  h 
curves  obtaining  curve  A'  B'  G  Y'  X'. 

p  _  9h    _  A  v  h 

8.8   ~      8.8 

The  output  power  curve  A  B  C0  Y  X  was  then  computed  by 

ghE 

8.8 

E  or  efficiency  for  each  point  was  obtained  from  the  characteristic 
curve  of  the  wheel,  Figure  245,  by  first  computing  from  the  known 


Graphical  Analysis. 


693 


values  of  q,  h,  and  S  (=  180)  at  each  point  the  values  of  the  dis- 
charge under  one  foot  head  and  <j>. 

Many  interesting  facts  can  now  be  seen  from  a  study  of  Figure  405 
It  will  be  seen  that  the  opening  or  closing  of  the  gate  in  order  to  in- 
crease, or  decrease,  the  power  of  the  wheel  has  an 'immediate  effect 
directly  opposite  to  that  intended  and  that  in  the  output  curve  the 


Fig,  405.  — Graphical  Analysis  of  Speed  Regulation. 

power  reduces  to  practically,  if  not  quite,  zero  for  nearly  one-half 
second.  The  effective  head  drops  very  greatly  during  acceleration, 
and  rises  during  retardation.  It  is  evident  that  the  rate  of  gate 
movement  here  used  (%  second)  is  too  fast  for  closure,  since  the 
head  rises  to  about  165  feet,  over  three  times  its  normal  value. 

Now,  since  the  product  of  power  and  time  gives  energy  or  work, 
it  is  evident  that  the  areas  of  the  figures  generated  by  the  ordinates 
to  the  various  load  curves  are  proportional  to  the  demand  for  en- 


694  Speed  Regulation. 

ergy  and  the  areas  of  the  output  curves  are  proportional  to  the 
supply.  The  area  between  the  two  curves,  therefore,  represents  a 
deficiency  or  excess  of  work  accomplished  by  the  wheel,  and  can 
be  measured  by  means  of  a  planimeter  or  otherwise.  The  value  of 
one  square  is  %  X  200=50  horse  power  seconds  =  to  Y  zzo  — 
27,500  foot  pounds. 

It  was  found  in  this  way  that  the  deficient  hydraulic  energy  sup- 
plied to  the  wheel,  assuming  the  load  demand  to  increase  from  14 
to  full  is 

27,500  X  areaB'  O  Y'  X'  C'  B' 
=  27,500  X  36 
=  990,000  foot  pounds. 

The  deficient  load  output  is 

27,500  X  areaB  C0  YXCB 
=  27,500  X  35  =  963,000  foot  pounds. 

This  deficiency  of  input  over  output  must  be  supplied  from  the 
energy  stored  in  the  rotating  parts,  or  from  the  fly-wheel  effect, 
and  can  be  accomplished  only  by  a  drop  in  speed  of  the  power  unit. 
Furthermore,  in  the  case  considered,  the  speed  can  never  return  to 
normal  as  long  as  the  load  remains  at  full  value,  but  suffers  a  per- 
manent drop  due  to  the  fact  that  v,  q,  h  and  power  theoretically 
approach,  but  never  equal  the  normal  values  for  the  new  gate 
opening. 

The  excess  energy,  when  the  load  again  drops  to  its  ^4  value  is, 
27,  500  X  area  C  E  F  A  B  C       or 
27,500  X  18  =  495,000  foot  pounds. 

It  is  evident  that  this  excess  energy  at  decreasing  load  will  al- 
ways be  less  than  the  deficient  energy  at  time  of  increasing  load, 
since  the  low  efficiency  of  the  wheel  during  the  velocity-change 
tends  to  decrease  the  former  and  increase  the  latter. 

It  is  also  possible  to  dissipate  the  excess  energy  through  a  by- 
pass or  relief  valve,  while  no  method  is  available  for  supplying  the 
deficiency  during  load  increase  except  at  a  sacrifice  of  the  kinetic 
energy  of  the  rotating  parts  and  consequent  reduction  of  speed. 

In  Section  226,  Chap.  XVIII,  it  was  shown  that  the  percentage 
departure  of  the  speed  from  normal  is 

*  =  294,000  R*K 


Since  the  deficient  energy  AK  is  actually  measured  in  this  case, 
the  estimated  co-efficient  R  becomes  unity.  The  normal  speed,  S, 
of  the  wheel  is  180,  and  I  will  be  assumed  as  1,000,000  ft.2  Ibs.,  or 
1,000,000  pounds  at  one  foot  radius,  then 


Numerical  Example.  695 

d  -  294  ooo          963'00° 

1,000,  000  X  ISO2 

=  8.7  per  cent. 

This  is  a  permanent  drop  in  speed. 

In  order  for  the  speed  to  pick  up  again  to  normal,  the  gate  must 
therefore  overrun.  The  condition  then  is  best  illustrated  by  assum- 
ing in  Figure  405  that  the  load  increases  only  to  0.8  of  full  load 
value,  following  the  line  A  B  D  D,  while  the  gate  movement  follows 
the  same  line  as  before.  In  this  case  the  v,  h,  wheel  imput,  and 
wheel  output  curves  will  be  unchanged. 

The  deficiency  of  input  or  of  energy  in  the  delivered  water  is  then 
(by  means  of  planimeter)  represented  by  area  B'  D'  Y'  Q  B'  or 

=  27,500  X  21.8  =  600,000  foot  pounds. 
The  deficiency  of  output,  represented  by  area  B  D  Y  C0  B,  is 

27,500  X  21.3  =  586,000  foot  pounds, 
giving  a  speed  regulation  of 


The  two  quantities  will  probably  always  agree  as  closely  as  the 
accuracy  of  the  problem  demands,  and  much  labor  can  be  saved  in 
an  analysis  if  hydraulic  horse  power,  or  input,  only  is  considered. 

At  Y  the  power  curve  crosses  the  demand  line,  D  D,  and  the 
speed  begins  to  pick  up,  due  to  an  excess  of  developed  power.  The 
time  required  for  return  to  normal  can  be  obtained  by  continuing 
the  two  curves  until  the  excess  area  equals  the  former  deficiency. 
In  this  case  8%  seconds  is  required. 

By  the  successive  application  of  equation  (41)  Chapter  XVIII  to 
narrow  vertical  strips  of  the  excess  or  deficient  energy  area,  we 
may  plat  the  speed  curve  of  the  unit.  In  this  way  curve  MSS±, 
Figure  405,  for  increase  from  !/4  to  Ml  load;  curve  MSS2  for  in- 
crease from  14  to  .8  load  but  simultaneous  full  gate  opening  ;  curve 
S'  S^  for  decrease  from  full  to  14  loaci>  and  curve  S'  S2  for  decrease 
from  full  to  45  per  cent,  load,  were  platted.  Curves  MSSX  and 
S'  Si  never  returned  to  normal  (180  R.  P.  M.),  but  curve  MSS2  re- 
turns in  8!/2  seconds,  and  curve  S'  S2  in  4  seconds- 

It  is  the  belief  of  the  writer  that  this  method  of  analysis  is  not  too 
long  for  a  problem  in  practice  and,  if  not,  is  therefore  better  than 
the  method  given  in  Chapter  XVIII  since  the  conditions  before 
and  during  gate  movement  can  be  readily  included. 


APPENDIX—  C. 

THE  STAND-PIPE. 

It  was  shown  in  Section  223,  Chapter  XVIII  that  the  following 
equations  apply  to  the  operation  of  a  plant  with  standpipe  : 

d.V        '    ST  2T 

(1)  -r-  =-y  (accelerating  head)  —  -y-  ha 

(<2\  d  dh         Av  ~ 


dt        dt  F 

The  value  of  ha  in  a  plant  with    penstock,   is 

ha  =  y  —  hf 

1  v3 

Hence  =  y  —  (1  -j-  f  ~r  -h  etc.)  —  =  y  —  cv2 


Equation  (2)  gives  the  instantaneous  rate  of  fluctuations  of  water 
level  in  the  stand-pipe. 

Equation  (3)  gives  the  rate  of  increase  of  penstock  velocity  in 
terms  of  the  then  existing  values  of  y  and  v. 

The  quantity,  q,  in  equation  (2),  represents  the  water  used  by  the 
wheel.  This  may  remain  practically  constant  if  the  head  fluctua- 
tion is  not  too  large,  in  which  case  the  speed  of  the  wheel  will  suffer  ; 
or,  by  means  of  an  ideal  action  of  the  governor,  it  may  be  made  to 
fluctuate  inversely  as  the  head  h,  thus  maintaining  a  constant  value 
of  the  product,  qh,  and  hence  of  the  power  input  of  the  wheel.  In 
case  this  latter  assumption  is  made,  then  : 

qh  =qt  h, 
or  q(H-y)=Av1(H-cv12) 

Substituting  this  value  of  q  in  equation  (2)  gives  : 
(4)  dy_A  r         YI  (H  -  o  vr*  n 

dt~FLV  (H-y)       J 

The  solution  of  the  two  simultaneous  differential  equations  2  and 
3,  or  3  and  4,  depending  upon  which  assumption  is  made,  is  nec- 
essary in  order  to  determine  the  exact  curve  of  variation  of  head 
and  velocity.  Their  general  solution  is  however,  very  difficult  if  not 
impossible  in  this  form.  The  equations  may  be  applied  successively 
to  short  portions  of  the  arc  by  considering  the  curves  to  consist  of 


Graphical  Analysis.  697 

a  great  many  short  straight  lines.  This  method  is  not  too  long  for 
application  to  a  problem  in  practice,  and  will  assist  in  obtaining  ap- 
proximate formulas  which  will  be  seen  to  coincide  very  closely  with 
the  true  curves. 

Assume  an  installation  where  d  =  8',  1  =  500'  H  =  50,  F  =  8A. 
Let  the  velocities  on  the  penstock  at  fractional  loads  be  the  same  as 
given  in  the  problem  considered  in  Section  228,  Chapter  XVIII.  If 
the  load  suddenly  increases  from  *4  to  full,  the  velocity  in  the  pen- 
stock must  accelerate  from  1.94  to  4.77  feet  per  second,  or  q  from 
97.8  to  240  cu.  ft.  per  sec. 

Estimating  f  =  .018,  equation  (3)  gives 
dv        32.15  F  .  500. 


(5)  -  =  .0643  (y  —  .0331  v2) 

Qt 

and  equation  (4)  gives  : 

dy_  _  dh  _  v       4  .  77  X  49  .  25 
"cfiT  ~  dt  ~¥~   8(H  —  y) 

<*}L  =  ±  _      29'4 
dt.        8         H  —  y 

Curves  Av  and  Ah,  Figure  406,  show  the  curves  of  velocity,  v,  and 
head,  h,  respectively,  obtained  by  applying  equations  (5)  and  (6) 
alternating  to  the  two  curves,  considering  them  to  remain  straight 
for  the  time  interval  between  consecutive  points  which  were  taken 
from  %  to  one  second  apart  depending  upon  the  curvature.  The 
closer  these  points  are  taken  the  more  accurate  would  be  the  result- 
ing curves. 

If  friction  in  the  penstock,  and  the  action  of  the  governor,  in 
compensating  for  the  fluctuations  of  h,  be  neglected  then  equations 
(i)  and  (2)  become 


(8)  =         v,-v 

Dividing  (8)  by  (7): 

dy  _  Al[  v,  —  y 
dv  ~~  Fg'       y 

Integrating: 


To  determine  the  constant  of  integration,  C  ;  let  v  =  v0  when 
y  =^=  o,  whence  : 


698  The  Stand-pipe. 

Substituting  this  value  in  (9)  gives  : 

(10)  y2  -  -—-  [(v,  -  v0)2  -  (Vl  -  v)*] 

Substituting  this  value  of  y  in  (7)  and  solving  for  dt  gives 


-  •  y(Tl_Vo_fVl_v). 
The  integral  of  (n)  is: 


When  t  =  o,  v  =  v0f  hence 

c= 

after  which  (12)  becomes: 


t= 


VT  —  v 
Solving  this  equation  for  v  gives: 

(13)  v  -  Vl  -  (Vl  -  v0)  cos  - 


If  this  value  of  v  be  now  substituted  in  equation  (8)  the  equation 
for  y  in  terms  of  t  can  be  obtained  as  follows  : 


When  y  =  o,  t  =  o,  hence  C  —  o  and 
^          04)          '     '  v  = 


Since  this  equation  is  that  of  a  true  sine  curve  it  will  be  readily 
seen  that  the  maximum  ordinate  and  hence  the  maximum  de- 
parture of  the  head  from  normal  is 

(15)  Y  =  ±-(Vl~Vo)' 


and  return  to  normal  head  occurs  when 


Whence 

(16)  T  = 


Fluctuations  of  Head  and  Velocity. 


699 


Equations  13  and  14  may  now  be  revised  to  read 


(17) 


(18) 


i  —  v0)  cos—  t 


and 


fr* 


These  equations,  (17)  and  (18),  are  shown  for  a  particular  prob- 
lem, by  the  dotted  lines  Bv  and  Bh  in  Figure  406.  The  closeness  of 
their  agreement  with  the  curves  Av  and  Ah  which  involve  the 
effect  of  both  friction  and  governor  action  shows  that  the  values 


IN  FEET  PENSTOCK  VELOCITY  IN  FEET  PER  SECOND 
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Fig.  406. —Curves  Showing  Fluctuations  of  Head  and  Penstock- Velocity 
in  a  Plant  Avith  Standpipe. 

T  and  Y  would  commonly  be  as  clo'se  to  the  truth  as  the  estimate 
could  be  made  of  the  probable  load  change  (vj  — v0),  for  which  the 
stand  pipe  should  be  designed. 

More  exact  formulas  can  be  derived,  however,  from  the  stand 
point  of  energy  as  follows : 

Let  the  time  required  to  reach  D'  and  hence  to  approximately 

TV 

reach  the  valve  v1?  under  exact  conditions,  be       • 


7oo  The  Stand-Pipe. 

T"  T 

The   time  -7-  will  be  slightly  greater  than  y'    when    friction    and 

governor  action  are  involved,  and  the  method  of  determining  it  will 
be  given  later  (equation  30). 

It  is  evident  that  the  number  of  foot  pounds  of  energy  which 

must  be  supplied  by  the  standpipe  in  this  time  ~  is  equal  to  the  en- 
ergy required  by  the  wheel  plus  that  required  to  accelerate  the  water 
in  the  penstock  plus  that  necessary  to  overcome  the  friction  of  the 
penstock  minus  that  supplied  through  the  penstock, 

(19)  Or  Es  =  Ew  +  Ea  +  E,—  Ep 
Now, 

(20)  Es  =  w  F  D'     H  -  cv02  — 


where  D'  is  the  maximum  surge  below  the  initial  friction  gradient 
for  Vo,  and  is  used  in  place  of  Y  to   distinguish    it  from   the  value 
obtained  by  the  other  formula:     •.  »" 
Also, 

(21)  Ew  =  A  v,^w  (H  —  CVl3)      and 

'   (22)  Ea--^-   Al(vi2-vo2) 

To  obtain  Ef  wre  have 

(23)  d  E,  =  A  v  w  X  cv2  dt 

where  c  is  the  friction  coefficient  and  v  is  obtained  from  equation(17). 

rp  ' 

The  integration  of  (23)  between  the  limits  t  =  -^  and  0,  gives, 

[vi8  T'         3  T' 
~2~       -^— v*2  (vi-vo)  + 

Tf 

Also  to  find  Ep  we  have 

dEp  =  HAwvdt, 

where  v  is  obtained  from  equation  (17)  as  before.      Integrating  be- 
tween the  limits  Y  and  0,  gives 

(25)  Ep  : 

Combining  and  simplifying: 

F    f  2«  L        ^ 

vi2  (vi  -  vo)  +  M  T^  vi  (vi  -  vo)2  -  ^-  ( vi  -  vo)8]  +  —. ~  (vi  -  vo) 


Maximum  Drop  in   Head.  7O1 

The  upward  surge  can  be  found  by  the  same  equation  by  a  proper 
change  of  signs,  but  is  unimportant  since  it  is  always  less  than  the 
downward  surge  Db  for  the  same  change  of  velocities. 

If  friction  be  omitted  and  T'  be  changed  to  T  for  reasons  men- 
tioned later,  equation  (26)  reduces  to 


(28)  D2  -  2HD  = 


-  ~     ~ 


~  (vi2  -  vo'2  )  +  ~  (vi  -  vo) 


To  derive  an  equation  for  the  maximum  upward  surge  Da,  when 
full  load  is  rejected,  we  may  equate  the  original  kinetic  energy  in 
the  penstock  to  that  expended  in  friction  plus  that  used  in  raising 
water  in  the  standpipe..  The  energy  lost  in  friction  is  found  from 
equation  (24)  by  putting  vx  =  o 

„       A  w  c  T  vo3 
or    Ef  =  —    — ^— 

The  other  quantities  are  evident.    This  gives : 

W.A  L  Awe  T  vo3         w  FE 

-  vo2  = r. —  H *- 


or 


Equations  (21),  (24),  (25)  and  (26)  are:  all  theoretically  exact 
except  for  the  assumption  that  the  velocity  change  takes  place  along 

TV 

a  simple  harmonic  in  time—.  The  true  curve  for  a  half  cycle,  as 
used,  is  scarcely  distinguishable  from  a  simple  harmonic  but  its 
period  T'  or  time  for  return  of  water  in  standpipe  to  normal  level  is 
greater  than  the  value  T,  given  by  equation  (7).  In  three  cases 
which  the  writer  has  solved  by  successively  applying  the  differen- 
tial equations  to  short  positions  of  the  arc  he  has  found  that  the 
true  value  T'  may  be  closely  approximated  by  the  following  for- 
mula : 

(30)  T'  =  5,T 

where  T  is  found  from  equation  (16), 
Y  from  equation  (15),  and 
D  from  equation  (28). 

The  quantity  T'  is  useful  in  itself  as  the  true  time  for  return  to- 
normal  head,  but  its  use  in  formula  (26)  for  determining  D'  is  not 
advisable,  as  the  writer  has  found  by  solving  a  number  of  problems 
that  the  value  of  D',  thus  found,  agrees  almost  exactly  with  the 
value  of  D  found  from  equation  (28),  in  which  equation  the  value  of 
T  from  equation  (16)  is  used.  Equation  (28)  is  therefore  offered  as 


702  The  Stand-Pipe. 

a  much  simpler  substitute  for  equation    (26)    and   equation    (27) 
becomes : 

(31)  Db  =  D  +  cvo2  * 

Like  all  wave  motions,  these  surge  waves  are  liable  to  pile  up,  one 
upon  another,  in  case  several  gate  movements  occur  at  proper  inter- 
vals and,  in  fact,  no  limit  can  be  placed  upon  the  possible  amplitude 
of  the  surge  which  can  occur  in  this  way.  In  a  plant  where  large 
frequent  load  changes  are  anticipated  the  danger  from  this  source 
should  receive  careful  attention.  Some  means  should  be  adopted 
for  causing  the  wave,  due  to  a  given  gate  movement,  to  rapidly 
subside  in  order  to  lessen  the  probability  of  its  combination  with 
another  wave.  One  method  of  accomplishing  this  result  is  by  ar- 
ranging the  standpipe  to  overflow  at  a  definite  elevation  above  the 
forebay.  This  limits  the  upward  surge  and  thereby  the  maximum 
possible  downward  surge  which  could  occur  under  any  assumption 
of  gate  movements.  This  method  necessitates  a  waste  of  water. 

Another  methodf  is  that  of  imposing  a  resistance  between  pen- 
stock and  standpipe.  This  not  only  causes  the  waves  to  subside 
more  rapidly  but  also,  if  properly  designed,  reduces  the  amplitude 
of  a  single  wave.  This  is  of  greatest  advantage  near  full  load  where 
the  downward  surge  is  apt  to  lower  the  head  sufficiently  to  make 
it  impossible  for  the  unit  to  deliver  the  required  power.  Another 
effect  of  the  resistance,  however,  is  to  change  the  form  of  the  curve 
of  effective  head  so  that,  instead  of  a  slow  sinuous  pressure  drop 
after  an  increase  of  load,  a  sudden  drop  is  obtained.  This  is  evi- 
dently opposed  to  good  speed  regulation  as  it  adds  to  the  effective 
sudden  load  for  which  the  governor  must  compensate  by  requiring 
a  greater  q  to  make  up,  not  only  for  the  increased  load,  but  also  for 
the  suddenly  decreased  head.** 

*Mr.  Raymond  D.  Johnson  in  Am.  Soc.  M.  E.  1908  has  derived  an  equation  for 
D  as  follows: 

D'2=AL    (Vl__voa   +    C2    (Vl8_vo.)« 

The  results  obtained  by  this  equation  agree  quite  closely  with  those  obtained 
by  the  writer's  method  and  the  two  entirely  independent  analyses  of  the  problem 
are  mutually  corroborative. 

fSee  paper  on  "Surge  Tanks  for  Water  Power  Plants"  by  R.  D.  Johnson 
with  discussions  by  the  writer  and  others  in  the  Trans.  Am.  Soc.  of  M.  E.  1908. 

**For  further  discussion  of  this  subject  and  a  mathematical  analysis  of  the 
problem  see  Mr.  R.  D.  Johnson's  paper  with  discussions  as  previously  re- 
ferred to. 


APPENDIX— D. 
TEST  DATA  OF  TURBINE  WATER  WHEELS. 

TABLE  LIX. 

Test  of  a  113-inch  Boott  Center  Vent   Turbine.     Built   in  \1849  for  tfie  Boott 
Cotton  Mills,  Lowell,  Mass.,  after  designs  by  James  B.  Francis. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part. 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

1  

0.25 
0.25 
0.25 
0.25 
0.25 
0.25 
0.25 
0.25 

0.50 
0.50 
0.50 
0.50 
0.50 
0.50 
0.50 
0.50 

0.75 
0.75 
0.75 
0.75 
0.75 
0.75 
0.75 
0.75 
0.75 
0.75 

1.00 
.00 

.00 
.00 
.00 
.00 
.00 
.00 
.00 
.00 
1.00 
1.00 
1.00 

0.603 
0.577 
0.5flO 
0.592 
0.596 
0.595 
0.598 
0.544 

0.756 
0.767 
0.775 
0.780 
0.785 
0.802 
0.815 
0.685 

0.852 
0.876 
0.893 
0.910 
0.913 
0.920 
0.922 
0.921 
0.925 
0.818 

1.000 
1.005 
1.000 
1.005 
1.006 
1.007 
1.006 
1.010 
1.017 
1.013 
0.982 
0.980 
0.887 

14.60 
14.67 
14.57 
14.16 
14.20 
14.14 
14.24 
14.30 

14.29 
14.23 
14.20 
14  19 
14.19 
13.78 
13.61 
13.95 

13.52 
13.37 
13.37 
13.40 
13.38 
13.34 
13.  32 
13.33 
13.30 
13.70 

13.40 
13.43 
13.33 
13.38 
13.39 
13.38 
13.36 
13.38 
13.40 
13.:-i2 
13.54 
13.57 
13.60 

4 

"  8 
17 
12 

7 
7 
8 

11 
10 
10 
8 
14 
11 
11 
8 

7 
2.5 
7 
9 
12 
9 
9 
9 
10 
8 

9 
6 
6 

7 
8 
8 
9 
8 
8 
8 
4 
2 
7 

35.6 

5:3.7 
43.4 
32.7 
30.0 
27.0 
25.25 
60.8 

60.6 
57.6 
55.9 
54.1 
51.4 
41.6 
35.9 
70.6 

66.3 
59.6 
54.1 
49.5 
47.2 
44.8 
43:5 
42.6 
41.9 
75.2 

42.5 

41.9 
40.7 
40.3 
39.6 
38.9 
38.1 
37  4 
36.8 
35.5 
0.0 
0.0 
77.0 

67.53 
64.89 
66.43 
66.61 
67.03 
66.89 
67.37 
61.08 

85.0 
86.35 
87.08 
87.69 
88.29 
90.17 
91.70 
77.11 

95.76 
98.49 
100.42 
10-'.  42 
102.82 
103.52 
103.77 
103.69 
104.23 
92.02 

112.53 
112.99 
112.56 
113.00 
113.07 
113.16 
113.09 
113.67 
114.29 
113.97 
110.45 
110.32 
99.8 

42.2 

21.94 
36.4 
40.8 
41.1 
40.0 
k'J.3 
0.0 

41.7 
52.4 

57.8 
62.7 
69.5 
82.0 
84.4 
0.0 

35.9 
65.3 
87.6 
102.2 
107.7 
111.2 
112.8 
114.0 
114.9 
0.0 

136.4 
137.0 
135.6 
136.6 
136.8 
136.9 
136.6 
136.5 
136.7 
134.5 
0.0 
0.0 
0  0 

37.7 
20.3 
33.2 
38,2 
38.1 
37.3 
27.0 
0.0 

30.3 
37.6 
41.3 
44.4 
48.9 
58.3 
59.6 
0.0 

24.5 
43.7 
57.6 
65.7 
69.0 
71.0 
72.0 
72.8 
73.1 
0.0 

79.7 
79.6 
79.7 
79.7 
79.7 
79.7 
79.8 
79.2 
78.7 
78.1 
0.0 
0.0 
0.0 

2  

3  
4  
5 

•6  

7  

8  
9  

10 

11  

12  
18  
14  

15  

16  ; 

17  
18  
19  
20  
21  

22  
23  

2t 

25 

26  

27  

28  

29  
30  

31     

.32  
33  

34     

35  

36  

37  
38  

39  

704 


Turbine  Test  Data. 


w  »  A 

3     H  * 


o  •- 

S    H 


S*I 


* 


III. 


Ho 


00     B     * 


II 


i 


1 


°- 

II 


111 

**  *"c 

111 


CM 


111 


.    2 


1-   t-_  OO  00  O 


00  OC  i  S3  OO  OO 


H  CJ  i-<  Tf«  IO  ' 


i— <  ck  r-  - 
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i  o  o  TH  01  •<*<      t^  O5  —  (N  co  co-g;  xo  i 
>«ft«2lOWU3        CO  CO  •*•<»'•<«<  Tj<  ^  r}<  • 


Ji-5^*'c4t^*J<pocotc*Cic^4< 


oo< 

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1  O  O  Y-H  ^  IA  t^>  1 

>  o>  r-  •*  3  «s  o  i 

>  rf  10  lA  GO  oi  10  c 

'  «^  t^- 1~  t-  t~  t- 1 


t>-  oo  «o  eo  o  «o  o»  oo  n  o  «o  oo  M  o  i-« 


Victor  Turbine. 


705 


OC' 

3  ©ooooo©      aoaooocsoaJcScj 

o  ©  ©  '       •     © • 

•  t^-t>-      o  P  t>  r-- 1>  t>- r- r-      <o  to  «o  01- S  t^cq  ^<ioio§33«o      w«e§5*'S^§^^§ 

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eo- ci     "eo    *  '    'c^i-eo    '     co oi      eo    '    *    "c4    *co    "    * 

6  «D  to  t-'  r-'       t--"  05  ©  ri  cq  CO  rf'  rjJ       •*'  to  r-'  06  OO  OS  C 

:>(»  o  o  o 

Kgg£S82§£§    SSsHlli 

l|  e'*^Si 

i  o  _•  i-i     in  • 

| =  .  =  s     S.  .....  s     jjj.  .  .  -  .  .  , 

43 


7o6 


Turbine  Test  Data. 


TABLE  LXI. 

Test  of  a  96-inch  Fourneyron   Turbine  Built  in  1851  for  the   Tremont  Mills, 
Lowell,  Mass.,  after  designs  by  James  B.  Francis. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part. 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

1  0 

1  01 

12  86 

8 

53  62 

139  42 

161  4 

78  4 

2 

1  0 

1  01 

12  86 

10 

53  5 

139  42 

159  2 

78  3 

3           

1  0 

1  01 

12  87 

10 

53  6 

139  47 

159  5 

78  4 

4 

1  0 

1  13 

12  55 

6 

95  8 

156  65 

60  6 

27  2 

5  ,.. 

1  0 

1  12 

12  61 

8 

91  9 

154  39 

77  9 

35  3 

6      

1  0 

1  10 

J2  6-"> 

7 

87  7 

152  27 

94  0 

43  0 

7 

1  0 

1  08 

12  70 

8;j  () 

149  46 

109  2 

50  7 

g 

o 

1  07 

12  72 

5 

78  5 

147  29 

l''l  5 

57  2 

9    

o 

1  OB 

12  18 

5 

77  4 

146  02 

131  7 

62  2 

10 

o 

1  05 

12  80 

g 

71  0 

144  81 

140  2 

66  7 

11 

o 

1  04 

12  82 

9 

67  5 

143  91 

147  2 

70  3 

12    

o 

9 

107  0 

0  0 

0  0 

13           .... 

o 

1  18 

12  51 

9 

lo7  o 

163  43 

0  0 

0  0 

14     

o 

1  03 

12  86 

9 

6t  0 

142  52 

152  6 

73  5 

15      

o 

1  03 

12  89 

9 

61  4 

142  04 

155  8 

75  0 

16 

o 

1  03 

12  89 

| 

60  0 

141  98 

157  0 

75  6 

17  

o 

1  02 

12  90 

9 

58  2 

141  28 

158  3 

76  6 

18           .... 

Q 

]  (J2 

12  8^ 

56  7 

140  47 

158  9 

77  4 

19  

o 

1  01 

12  88 

10 

55  4 

140  OS 

159  5 

77  9 

20  

o 

1  01 

12  87 

9 

54  7 

140  01 

159  7 

78  0 

21  
22 

.0 

o 

1.01 

1  01 

J2.90 
12  90 

10 
14 

54.1 
53  8 

139.90 
139  67 

160.0 
"160  2 

78.1 
78  4 

23  

(J 

1  17 

12  43 

9 

106  8 

161  69 

0  0 

0  0 

24            

o 

1  01 

12  90 

9 

53  6 

139  01 

160  5 

78  9 

25  
26  

.0 

o 

1.01 
1  0 

12.90 
12  89 

13 
5 

53.1 
52  5 

139.03 
138  76 

160.4 
159  5 

78.8 
78  6 

27  

28 

.0 

o 

1.0 
1  0 

12.90 
12  91 

14 
13 

5^.8 
52  4 

138.85 
138  87 

160.5 
160  5 

79.0 
78  9 

29... 

o 

1  0 

12  91 

12 

52  0 

138  51 

160  6 

79  2 

30  
31 

.0 

o 

1.0 
1  17 

12.90 
12  54 

]2 
y 

51.1 

106  8 

138!  19 
162  32 

160.5 
0  0 

79.4 
0  0 

32  

(J 

1  0 

12  91 

6 

£0  2 

138  27 

160  6 

79  3 

33 

o 

1  0 

12  93 

10 

48  8 

138  23 

160  6 

79  2 

34 

1  0 

1  0 

12  94 

jj 

47  1 

38  09 

160  0 

78  Q 

35  

1  0 

1  0 

12  94 

11 

44  5 

137  71 

158  4 

78  3 

36     

1  0 

0  99 

12  96 

jl 

41  7 

136  49 

156  2 

77  9 

37 

1  0 

0  98 

12  94 

10 

38  7 

135  14 

152  6 

77  0 

38  

1  0 

1  17 

12  5 

9 

107  1 

161  69 

0  0 

0  0 

39  

1  0 

0  98 

12  96 

12 

38  8 

135  34 

153  0 

76  9 

40  
41  

1.0 
1  0 

0.97 
0  97 

12.97 
12  98 

8 
11 

36.0 
31  9 

134.80 
133  75 

149.3 
142  7 

75.3 
72  5 

42  

1  0 

0  97 

12  95 

9 

27  3 

133  43 

133  0 

67  9 

43  
44  

1.0 
I  0 

0.9* 
0  98 

12.80 
12  77 

1.5 
2  5 

0.0 
0  0 

135.65 
135  62 

0.0 
0  0 

0.0 
0  0 

45  

1  0 

I  17 

12  47 

9 

106  9 

162  02 

0  0 

0  0 

46  
47 

1.0 
1  0 

1.00 
1  00 

12.95 
)«>  93 

11 
10 

49.9 
4Q  0 

138.62 

1  'Itf   nfl 

161.1 
IfiO  7 

79.1 
TQ  1 

48  

1  0 

1  00 

12  95 

11 

48  2 

138  47 

160  5 

78  9 

49  

1  0 

1  00 

12  95 

12 

47  4- 

•ifta   07 

160  3 

78  9 

50  
51 

1.0 
0  75 

1.00 
1   fl-t 

12.95 
12  7fi 

11 

j 

46.2 

138.16 

159.8 

78.7 

52  

0  75 

1   111 

!'•*  87 

g 

7*    A 

-IQQ    01 

120  fi 

K.Q     A 

53  

0  75 

1  00 

12  91 

9 

K7     ^ 

54.   . 

0  75 

1  00 

12  Q4. 

55  
56 

0.75 
0  7") 

0.99 

OQH 

12.95 

8 

61.4 

137.00 

145.9 

72.5 

0  75 

58  

0  75 

0  97 

•JO    QQ 

59  

0  75 

0  96 

iq   An 

60 

0  75 

61 

0  75 

OQK 

148.7 

Francis'  Tremont  Turbine. 


707 


TABLE  LXL—  Continued. 

Test  of  a  96-inch  Fourneyron   Turbine  Built  in  1851  for   the  Tremont 
Lowell,  Mass.,  after  designs  by  James  B.  Francis. 


Mills, 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficienc3'  =  l). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

91 

3 

4 

5 

6 

7 

8 

9 

62... 

0  75 

0  95 

13  04 

9 

46  3 

130  99 

147  9 

76  4 

63  

U  75 

0  95 

13  03 

8 

42  5 

13(1  89 

145  1 

75  0 

64 

0  75 

1  08 

12  72 

U 

103  0 

fl  fl 

n  (I 

65 

0  49 

0  88 

13  17 

H 

92  9 

121  97 

0  0 

0  0 

66  
67.     .. 

0.49 
0  49 

0.86 
0  8t 

13.08 
14  13 

6 
6 

81.1 
73  1 

118.55 
116  1 

52.8 
78  3 

30.0 
45  3 

68 

0  49 

0  83 

13  18 

g 

65  0 

114  26 

96  6 

69     

0  49 

0  82 

13  21 

60  2 

113  24 

103  3 

60  9 

70 

0  49 

0  81 

13  25 

y 

55  4 

111  52 

63  7 

71  

0  49 

0  79 

13  2d 

50  6 

109  71 

107  8 

65  2 

72  
73  

0.49 
0  49 

0.78 
0  78 

13.31 
13  31 

II 

6 

46.5 
46  5 

108.05 
107  95 

106.8 
107  0 

65.5 
65  6 

74  

0  49 

0  76 

13  33 

9 

41  2 

105  53 

102  3 

64  1 

75 

0  49 

0  75« 

13  36 

(s 

36  9 

103  85 

97  3 

61   9 

76  

0  49 

0  73 

13  41 

27  4 

100  54 

83  7 

54  8 

77... 

0  87 

0  99 

12  88 

51  3 

137  36 

156  8 

78  1 

78  

79 

0.87 
0  87 

0.99 
0  99 

12.90 
12  91 

7 

7 

49.3 
47  4 

136.97 
136  55 

157.0 
156  6 

78.4 
78  3 

80  
81  

0.25 
0  25 

0.58 
0  57 

13.35 
13  37 

5 
6 

74.9 

68  8 

80.45 

78  84 

0.0 
168  2 

0.0 
14  i 

82  
83  

0.25 
U  25 

0.56 
0.54 

13.40 
13  43 

6 

6 

57.6 
46  3 

76.62 
74  06 

38.6 

49  7 

33.2 
44  0 

84  
85  

0.2.') 
0.25 

0.52 
0  51 

13.48 
13  51 

8 
8 

40.3 
33  6 

71.87 
70  01 

50.9 

48  8 

46.3 
45  5 

86.   .'.. 

0  25 

0  49 

13  56 

27  7 

67  82 

44  4 

42  7 

87  

0.25 

0.47 

13.56 

H 

18  0 

64.51 

32  7 

33  o 

88  

0  25 

0  44 

13  52 

0  0 

60  36 

0  0 

0  U 

89  

90  
91  

0.25 

0.087 
0.087 

0.44 

0.28 
0.28 

13.53 

13.98 
14.00 

7 
7 

0.0 

37.2 
41.3 

60.42 

38.22 
38  57 

0.0 

9.09 
6  23 

0.0 

15.0 
10  2 

92        ... 

O.U87 

0.27 

14  02 

17 

23  3 

37  17 

14  21 

24  0 

7o8 


Turbine  Test' Data. 


TABLE  LXII. 

Test  of  a  57-inch  Left  Hand  McCormick  Turbine.  Built  by  J.  and  W.  Jolly, 
Holyoke,  Mass.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  Tested  on 
Conical  Draft  Tube.  Test  No.  1156.  Oct.  31  and  Nov.  1,  1898. 

With  the  flume  empty  a  strain  of  IT  Ibs.  applied  3.6  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  l). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

40 

000 

1  Oil 

13  77 

4 

79  87 

244  50 

305  SO 

80  10 

39 

OUO 

1  007 

13  86 

4 

83.25 

244  34 

309  12 

»0  49 

38  
37  

.000 
OUO 

1.004 
1  001 

13.92 
13  93 

4 
4 

86.75 
HO.  25 

244.16 
243.38 

311.49 
311.78 

80  82 
81.10 

36  

OUO 

0  994 

14  03 

4 

94  62 

242  58 

312  08 

80  86 

35  
3J 

.000 
0  770 

0.934 
0  890 

14.10 
14  69 

4 
4 

99.87 
79  37 

240.66 
222  19 

305.63 
299  03 

79  43 

80  81 

33  
32  
31   

0.770 
0.770 
0  770 

0.886 
0.883 
0  881 

14.72 
14.73 
14  75 

4 
4 

4 

82.87 
85.75 
88  75 

221.41 

220.81 
220  38 

302.63 
303.24 
'303  58 

81.89 
82.22 
82  36 

30  
29  
28     

0.770 
0.770 
0  770 

0.876 

0.868 
0  857 

14.76 

14.82 
14  86 

4 
4 
5 

92.00 
95.50 
98  90 

219.17 
217.65 
215  23 

302.19 

298.75 
292  57 

82.38 
81.68 
80  67 

27 

0  770 

0  847 

14  94 

5 

101  50 

213  41 

283  (JO 

78  28 

26... 

0  615 

0  762 

15  36 

4 

77  75 

194  56 

261  73 

77  23 

25  
24  

0.615 
0  615 

0.761 
0  757 

15.36 
15  40 

4 
5 

81.87 
86  20 

194.25 
193  52 

266.69 
269  07 

78.82 
79  62 

23  

0  615 

0  753 

15  39 

4 

89  62 

192  50 

267  55 

79  64 

22  
21  
20  

0.615 
0.615 
0  615 

0.745 
0.739 
0  729 

15.45 
15.47 
15  52 

4 
4 
4 

92.37 
95.62 
98  75 

190.92 
189.30 
187  15 

262.57 
257.51 
251  16 

78.50 
77.51 
76  26 

19  

18... 
17... 

0.615 

0.483 
0  483 

0.719 

0.632 
0  630 

15.63 

15.90 
15  87 

4 

4 
4 

102.25 

78.12 

82  37 

185.14 

164.25 
163  42 

243.37 

215.69 
218  46 

74.17 

72.83 
74  28 

16 

0  483 

0  626 

15  85 

4 

8(3  37 

162  32 

°17  32 

74  49 

15  
14  
13  

12 

0.483 
0.483 
0.483 
0  483 

0.621 
0.615 
0.609 
0  603 

15.81 
15.81 
15.74 
15  75 

4 
4 
4 
4 

89.50 
93.00 
96.00 
99  25 

160.80 
159.31 
157.40 
156  03 

213.03 
208.71 
20-3.38 
195  74 

73.90 
73.07 
72.04 
70  y4 

11  

0  483 

0  598 

15  7° 

4 

102  37 

154  55 

187*97 

68  23 

10  

0  483 

0  59'{ 

15  76 

105  50 

153  45 

179  36 

65  41 

9  
8  

0.360 
0  360 

0.500 
0  498 

16.27 
16  37 

4 
4 

74.  7o 

79  62 

131.52 
131  26 

161.14 
163  52 

66.41 
67  11 

7  
6  
5  
4 

0.360 
0.360 
0.360 
0  360 

0.495 
0.492 

0.488 

OAQZ 

16.42 
16.41 
16.43 

Ifi  4? 

4 
4 
4 

83.75 
87.12 
90.37 

130.63 
129.75 

128.87 

163.46 
161.15 
157.94 

67.20 
66.74 
65.78 
R4.  49 

3  

0  360 

0  481 

16  45 

96  62 

127  21 

14Q     -IK 

62  86 

2  

0  360 

0  479 

Ifi  ^4. 

-IAA     OX 

128  K^ 

611  19 

1  

0.360 

0.474 

16  59 

4 

104.37 

125.70 

134.86 

57.03 

Samson  Turbine. 


709 


TABLE  LXIII. 

Test  of  56-inch  Right  Hand  Samson  Turbine,  built  by  James  Leffel  Co.',  Spring- 
field, O.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  Test  No.  1257. 
June  20,  1900.  Tested  on  Conical  Cylinder. 

With  the  flume  empty  a  strain  of  22  Ibs.  applied  3.6  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

•4 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

9 

82.29 
83.26 
83.  5* 
82.79 
81.68 
78.94 

83.75 
84.60 

83.  ',13 
82.50 
80.63 
78  94 

84.32 
85.01 

84.24 
83  .14 
8:4.10 
80.41 

78.75 

84.08 
83.56 
82.40 
81  46 
K).56 
79.78 

80.74 
81.06 
80.99 
80.31 
79.29 

80.06 
80.36 
79.85 
78.70 
77.01 

78.29 
78.33 
78.09 
77.40 
75.99 
73.62 

75.00 
74.20 
73.11 
71.85 
70.20 
66.96 

1 

3 

4 

it 

C 

7 

8 

19... 

1.000 
1.000 
1.000 
1.000 
1.000 
1.  000 

0.919 
0  919 
0.919 
0.919 
0.919 
0.919 

0.846 
0.846 
0.846 
0.846 
0.846 
0.846 
0.846 

0.771 
0.771 
0.771 
0.771 
0  771 
0.771 

0.696 
0.696 
0.696 
0.696 
0  696 

0.626 
0.626 
0.626 
0.626 
0.626 

0.564 
0.564 
0.564 
0.564 
0  564 
0  564 

0.497 
0.497 
0.497 
0.497 
0.497 
0.497 

0.995 
0.996 
1.001 
0.999 
0.992 
0.980 

0.945 
0.947 
0.943, 
0.936 
0.928 
0.916 

0>'85 
0.888 
0.882 
0.876 
0.868 
0.855 
0  843 

0.824 
0.819 
0.812 
0.802 
0.794 
0.786 

0.736 
0.727 
0.725 
0.717 
0.715 

0.663 
(1.660 
0.655 
0.651 
0.647 

0.603 
0.600 
0.598 
0.592 
0.587 
0.581 

0.537 
0.532 
0.527 
0.522 
0.520 
0.517 

13.27 
13.27 
13.27 
13.30 
13.33 
13.50 

13.52 
13.50 
13.52 
13.56 
13.63 
.13.71 

13.80 
13.79 
13.80 
13.82 
13.91 
14.09 
14.11 

14.15 
14.18 
14.21 
14.24 
14.27 
14.33 

14.63 
14.69 
14.70 
14.76 
14.81 

15.11 
15.12 
15.16 
15.13 
15.17 

15.45 
15.44 
15.46 
15.49 
15.  5t 
15.56 

15.91 
15.95 
16.00 
16.04 
16.04 
16.07 

3 
4 
4 
4 
4 
4 

4 
4 

4 

4 

4 

4 
4 
4 
4 
5 
4 
4 

4 
4 
4 
4 
4 
3 

4 
4 
4 
4 
4 

4 
4 
4 
4 
4 

4 
4 
4 
4 
4 
4 

4 
4 
5 
4 

4 
4 

99.67 
104.00 
108.62 
111.75 
113.50 
117.00 

99.37 
104.25 
107.75 
110.12 
132.37 
115.12 

96.62 
101.00 
103.12 
105.00 
107.80 
110.87 
113.50 

97.50 
1(10.37 
102.12 
104.00 
106.25 
109.67 

97.50 
100.37 
103.75 
106.87 
110.50 

98  25 
102.00 
105.00 
107  37 
110.75 

95.50 
98.62 
102.25 
105.75 
109.87 
114.00 

101.25 
105.12 
109.20 
113.37 
117.50 
125.75 

245.41 
245.75 
246  86 
246.69 
245.26 
243.81 

2:35.43 
235.56 
234.80 
2X3.37 
231.98 
229.82 

222.77 
223.37 
2<21.99 
220.47 
219.26 
217.31 
214.58 

210.02 
208.95 
207.29 
205.01 
203.03 
201.51 

190.73 
188.70 
188.28 
186.67 
166.38 

174.50 
173.83 
172.83 
171.55 
170.70 

160.63 
159.54 
159.11 
157.75 
156.65 
155.30 

145.14 
143.93 
142.87 
141.70 
140.91 
140.27 

303.28 
307.27 
309.85 
307.40 
302.19 
294.03 

301.69 
304.47 
301.52 
295.43 

*88.50 
281.48 

293.34 
296.35 
292.06 
286.69 
283.35 
278.62 
269.81 

282.77 
280.18 
274.66 
269.13 
264.12 
260.71 

254.95 
254.28 
253.68 
250.42 
247.67 

238.90 
239.01 
236.77 
231.17 
225.66 

219.89 
218.36 
217.37 
214.04 
208.95 
201.31 

195.99 
192.77 
189.13 
184.80 
179.56 
170.82 

18  
17  

}(j  

15  
14  

25  

24     

23  
22  

21 

5>0  

32  
31  

30        

29 

28  
27  
26  

54  
53  

52 

51 

50       

49 

48  
47  

46  ..     . 

45  
44  

43 

42  
41.  
40  

39  

38  

37          

36  
35  

34  
33 

6     

5  
4  

3  
2 

\ 

Turbine  Test  Data. 


TABLE  LXIV. 

Test  of  a  54-inch  Right  Hand  Special  Hercules  Turbine.  Built  by  the  Holyoke 
Machine  Co.,  Holyoke,  Mass.  Testing  Flume  of  the  Holyoke  Water  Power 
Co.  No.  1051.  Date  Nov.  12,  1897. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
(discharge 
discharge 
at  full  gate 
with  highest 
efficiency  =1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet, 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

42     
41  

1.000 
1  000 

1.004 
997 

13.98 
14  07 

5 
4 

80.40 
84  12 

230.06 

228  98 

305  38 
306  94 

83.72 

84  00 

40  
39 

l.OUO 
1  000 

.989 
881 

14.13 
14  22 

4 

4 

87.00 
90  50 

227.80 
°26  71 

305.62 
305  62 

83.71 
83  58 

38  

1  000 

974 

14  26 

4 

94  00 

225  30 

303  89 

83  26 

37  
36  

1.000 
1  000 

.964 
956 

14.29 
14  34 

4 
4 

98.00 
101  50 

223.16 

221  65 

299.65 
293  11 

82.83 
81  31 

35  

1  000 

944 

14  38 

4 

104  87 

219  38 

285  03 

79  66 

34  

800 

881 

14  69 

4 

80  00 

206  93 

287  01 

83  25 

33  

800 

875 

14  73 

5 

83  20 

205  72 

287  19 

83  56 

32  
31  

.800 
800 

.868 
859 

14.80 
14  87 

4 
4 

86.  6  J 
90  25 

204.66 
202  ^8 

V87.16 
286  38 

83.59 
83  65 

30     

800 

852 

14  94 

4 

93  75 

201  77 

284  75 

83  28 

29 

800 

844 

15  01 

4 

97  12 

200  41 

281  78 

82  59 

28  

800 

836 

15  07 

4 

101  00 

198  92 

277  94 

81  75 

27      

SOU 

829 

15  09 

4 

104  87 

197  26 

270  78 

80  20 

26 

800 

820 

15  15 

108  40 

195  46 

261  48 

77  85 

25      

650 

749 

15  38 

5 

77  oo 

179  88 

246  9") 

78  70 

24 

650 

745 

15  40 

fj 

81  00 

179  02 

250  4'' 

80  09 

23  
22       

.650 
650 

.739 
734 

15.45 

15  48 

o 
5 

84.60 
88  60 

177.87 
176  85 

251.78 
252  85 

8(1.78 
81  43 

21  
20  
iy  

.650 
.650 
650 

.728 
.722 
714 

15.49 
15.47 
15  50 

5 

92.80 
95.80 
99  25 

175.59 
173.91 
172  09 

252.22 
248.01 
''4'*  10 

81.76 
81.28 
80  02 

18  
17  

16 

.650 
.650 

527 

.705 
.696 

622 

15.53 
15.57 

15  97 

5 
4 

4 

102.40 
105.75 

74  50 

170.10 
168.14 

ic9  97 

234.48 
226.34 

20°  49 

78.26 
76.23 

7Q  40 

15  

.527 

618 

16  01 

4 

78  87 

151  47 

205  79 

74  82 

14  
13 

.527 
527 

.612 
606 

16.03 
16  09 

4 
4 

83.12 
87  25 

150.12 

207.28 
207  50 

75.94 

12 

527 

597 

16  12 

7tt  J.7 

11  

527 

591 

16  15 

95  37 

145  60 

200  89 

75  32 

10  

527 

584 

16  22 

4 

99  25 

14S  98 

195  57 

70  04. 

y 

527 

578 

16  23 

irvj   nn 

79  01 

8 

410 

4QQ 

410 

494 

16  63 

Sl     »'»" 

ifiO    t;i 

6.  ..    . 

410 

489 

Ifi    t'A 

5  
4  

.410 
410 

.483 
478 

16.68 
16  66 

4 

90.50 

04.    7& 

120.82 

159.88 

69.95 

3  
2  

.410 
410 

.472 
467 

16.68 

Ifi    7i 

5 

99.10 

118.20 

148.14 

66.25 

1  

.410 

.460 

16.79 

5 

109.30 

115.53 

129.97 

59.07 

McCormick  Turbine. 


711 


TABLE  LXV. 

Test  of  a  51-inch  Left  Hand  McCormick  Turbine.  Built  by  J.  and 
Holyoke,  Mass.  Testing  Flume  of  the  Holyoke  Water  Power  Co. 
1444,  Feb.  19  and  20,  1903.  Tested  on  Conical  Draft  Tube. 


W.  Jolly, 
Test  No. 


With  the  flume  empty  a  strain  of  37  Ibs.  applied  3.6  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

57  
55  

l.QOO 
1  000 

1.007 
1  001 

15.20 
14  71 

4 
4 

98.50 
101  12 

196.58 
192  30 

293.50 
278  13 

86.61 
86  70 

54 

1  ODO 

0  ij;  is 

14  70 

4 

105  50 

191  60 

277  38 

86  84 

53  

1  000 

0  995 

14  68 

4 

110  00 

191  02 

274  38 

86  28 

52  

1  (100 

0  989 

14  65 

4 

113  75 

189  58 

268.40 

85  21 

51  
50  

1.000 
1  000 

0.974 
0  948 

14.74 
14  86 

4 
4 

118.25 
124  25 

187.26 
183  09 

','55.10 
234  54 

81.49 
76  01 

49 

1  000 

0  922 

15  04 

4 

130  25 

179  05 

210  74 

69  00 

48  

1  000 

0  897 

15  15 

4 

136  00 

174  79 

183  37 

61  06 

75.''!!.'.'!!.'! 

0.760 
0.760 

0.879 
0  876 

15.65 
15  65 

4 
4 

90.50 
96  50 

174.22 
173  55 

259.30 
263  47 

83.86 
85  54 

74  
73  

0.760 
0.760 

0.871 
0.861 

15.67 
15.76 

4 
.4 

101.75 
106  00 

172.71 
171  13 

264.09 
260  83 

86.04 

85  28 

72  

71 

0.710 
0  76d 

0.850 
0  840 

15.83 
15  94 

4 
4 

110.75 
114  25 

169.47 
168  07 

257.58 
250  32 

84.66 
82  39 

70  
69  
68  

0.760 
0.760 
0.760 

0.826 
0.813 
0.795 

16.04 
16.16 
16.29 

4 
6 
3 

118.50 
123.17 
129  00 

165.73 
163.65 
160  65 

239.66 
228.35 

208  72 

79.50 
76.14 
70  32 

67  

0  760 

0  778 

15  74 

4 

132  25 

154  65 

178  31 

64  59 

85  

0.624 

0.767 

15.63 

4 

90.00 

151  93 

218  42 

81  11 

84  
83  

0.624 
0.624 

0.764 
0.756 

15.61 
15.64 

4 
4 

94.75 
100.25 

151.12 
149.67 

219.73 
218  97 

82.13 

82  48 

82  

0.624 

0.742 

15.67 

4 

104  25 

147  07 

213  65 

81  75 

81  
80  

0.624 
0.6.'4 

0.735 
0.7^4 

15.73 

15.78 

4 
4 

108.75 
114.25 

145.93 
144.08 

206.74 
200  26 

79.42 
77  67 

79 

0  624 

0.712 

15.86 

4 

119  75 

141  98 

189  71 

74  29 

78  

0.624 

0.698 

15.96 

4 

127.50 

139  76 

171.91 

67  96 

77  

0.624 

0.684 

16.12 

4 

134.75 

137.55 

145  35 

57  80 

47 

0  500 

0  656 

15  93 

.     4 

87  00 

131  12 

178  30 

75  27 

46  

0.500 

0.653 

15.96 

ft 

91.83 

13H.61 

179  53 

75  94 

45 

0  500 

0.648 

16  05 

4 

97  12 

130  11 

180  05 

76  03 

44  

0.5110 

0.640 

16.14 

4 

101.62 

128.70 

178.12 

75  61 

43     ..     .      . 

0.500 

0.632 

16.19 

4 

106.00 

127  55 

175  08 

74  76 

42  

0.500 

0.624 

16.25 

4 

111.50 

126.04 

169.13 

72  81 

41  

0.500 

0.615 

16.27 

5 

118.20 

124.29 

159.37 

69  49 

40  
39  

0.500 
0.500 

0.605 
0.59t 

16.30 
16.36 

4 
5 

124.00 
129.80 

122.26 
120.27 

146.29 
131.26 

64.73 
58.82 

38     

0.5UO 

U.585 

16.41 

6 

135.50 

118  65 

114.18 

51  71 

712 


Turbine  Test  Data. 


TABLE  LXVI. 

Test  of  a  45-inch  Right  Hand  Victor  Turbine.  Built  by  the  Plait  Iron  Works 
Co.,  Dayton,  Ohio.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  Test 
No.  1177,  March  13  and  14,  1899.  Tested  on  Conical  Draft  Tube. 

With  the  flume  empty  a  strain  of  10  Ibs.  applied  3.6  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi 

clency. 

.  1 

2 

3 

4 

5 

6 

7 

8 

9 

48  
47     

.000 

o;K) 

1.012 
1.000 

15.22 
15.21 

4 

4 

102.37 
107.50 

180.69 
180.24 

252.39 

254.82 

80.92 
81.96 

46 

000 

1  004 

15.20 

4 

111.50 

179.26 

253.70 

82.10 

45  
44          

.000 
000 

0.997 
0.986 

15.2(5 
15.31 

4 
5 

116.67 
121.60 

178.26 
176.54 

253.57 
*51.08 

82.19 
81.91 

43 

000 

0  972 

15.35 

4 

126.25 

174.41 

246.10 

81  .05 

42  

.000 

0.954 

15.36 

5 

128.40 

171.19 

235.46 

78.96 

41     

1  000 

0.934 

15.44 

4 

131.50 

167.98 

223.29 

75.91 

40... 

0.900 

0.959 

15.32 

4 

98.37 

171.76 

239.19 

80.15 

39    

0.900 

0.955 

15.32 

4 

103.37 

171.19 

241.52 

81.20 

38  
37  
36     

0.900 
0.900 
0  900 

0.949 
0.942 
0  929 

15.36 
15.39 
15.50 

4 
5 
5 

107.25 
111.30 
115.80 

170.19 
169.23 
167.41 

240.39 
239.64 
238.31 

81.08 
81.13 
80.98 

35 

0  900 

0  917 

15  54 

4 

119  00 

165  39 

234.39 

80.41 

34  
33     

0.900 
0  900 

0.907 
0  896 

15.58 
15.73 

4 
4 

122.50 
127.50 

163.86 
162.75 

230.47 
225.15 

79.60 
77.55 

32  
30  

0.900 
0  800 

0.890 
0  888 

15.73 
15.90 

4 
4 

133.50 
97.25 

161.52 
162.07 

217.62 

228.54 

75.52 

78.20 

29  
28  
27  

0.800 
0.800 
0  800 

0.886 
0.878 
0  867 

16.04 
16.20 
16  34 

5 
4 
4 

105.70 
111.00 
118.00 

162.46 
161.79 
lliO.41 

238.35 
239.74 
241.24 

80.65 
80.65 
81  15 

31 

0  800 

0  873 

1(5  80 

4 

113  37 

158  91 

231  00 

81  12 

26  
25     

0.800 
0  800 

0.861 
0  838 

16.24 

16  28 

4 
4 

131.35 
125  25 

157.14 
154  81 

232.71 
225.44 

80.32 

78  87 

24  

0.800 

0.826 

16.20 

4 

131.87 

152.24 

214.96 

76.85 

23.   . 

0  700 

0  802 

16  16 

4 

99  00 

147  56 

205.08 

75.83 

22 

0  700 

0  799 

16  15 

4 

104  12 

147  04 

207  20 

76  94 

21  

0.700 

0  794 

16.17 

4 

109.62 

146.23 

208  47 

77.74 

20  . 

0  700 

0  781 

16  12 

4 

114  50 

143  56 

206.09 

78  52 

19 

0  700 

0  768 

16  18 

4 

118  00 

141  49 

200  36 

77  17 

18  

17 

0.700 
0  700 

0.758 
0  747 

16.19 
16  23 

4 
3 

122.75 
130  00 

139.54 

137  72 

184.26 
185  42 

75.82 
73  14 

16  

0.600 

0.701 

16  39 

4 

96  00 

129.89 

169.53 

70.21 

15  

0  600 

0  702 

16  39 

4 

101  37 

130.02 

172  13 

71  22 

14  
13  

0.600 
0.600 

0.696 
0.683 

16.38 
16.44 

4 
4 

106.75 
111.62 

128.88 
126.85 

173.29 
172.85 

72.38 
73.08 

12    

0  600 

0  676 

16  44 

4 

115  50 

125  45 

170  23 

72-78 

11  
10  

0.600 
0.600 

0.669 
0.662 

16.42 
16.43 

4 
4 

118.87 
124.50 

124.06 
122.81 

165.94 
160.66 

71.82 
70.21 

9  

8 

0.600 
0  502 

0.656 
0  607 

16.44 
16  60 

4 
4 

131.25 
95  25 

121.81 
113  21 

151.55 
139  09 

66.73 
65  26 

7  

0.502 

0.603 

16  60 

4 

100.62 

112.49 

140.10 

66.15 

6  

0  502 

0  594 

16  64 

4 

104  62 

110  91 

139  27 

66  54 

5  
4 

0.502 
0  502 

0  586 
0  580 

16.62 
16  62 

4 
5 

109.75 
114  80 

109.32 
108  25 

138.65 
136  45 

67.29 

66  87 

3  

0.502 

0  576 

16  65 

4 

120  00 

107  66 

132  85 

65  35 

2  

0  502 

0  574 

16  68 

4 

125  50 

107  30 

127  86 

62  99 

1.   . 

0  502 

0  570 

16  68 

4 

131  50 

106  59 

120  58 

59  80 

Samson  Turbine. 


713 


TABLE  LXVII. 

Tent  of  a  45-inch  Right  Hand  Samson  Turbine.  Built  by  The  James  Leffel  Co., 
Springfield,  Ohio.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  Test 
No.  979.  Jan.  25  and  26,  1897.  Tested  with  Conical  Cylinder 

With  the  flume  empty  a  strain  of  15  Ibs.  applied  3.6  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
;ions  per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

8  

1  000 

0  992 

14  94 

5 

127.60 

171.24 

233  49 

80.48 

1  000 

1  000 

14  88 

5 

133.40 

172.12 

236  84 

81  54 

6  

1.000 

0.998 

14.92 

4 

138.12 

172.12 

238.65 

81.94 

5  
4 

1.000 
1  000 

0.999  ' 
1  001 

15.00 
15  02 

4 
4 

144.00 
148  75 

172.69 
173  23 

240.97 

240  82 

82.03 
81  61 

3     

1  000 

1.002 

15.03 

3 

153.33 

173.38 

239.89 

81  18 

2 

1  000 

0  998 

15  04 

4 

157  75 

172  81 

236  08 

80  09 

1  

18  
17  

1.000 

0.832 
0  832 

0.986 

0.887 
0  892 

15.11 

14.99 
15.02 

3 

4 
4 

169.33 

112.50 
119.75 

171.11 

153.24 
154.34 

218.85 

208.16 
215.05 

74.64 

79.90 

81  80 

16  
15  

0.832 
0.832 

0.896 
0  897 

15.04 
15.03 

4 

4 

126.12 
132.25 

155.04 
155.27 

219.62 
223.11 

83.05 
84  30 

14 

0  832 

0  896 

15.04 

4 

134.12 

155  03 

223.61 

84  55 

13  

0.832 

0.893 

15.06 

4 

143.00 

154.74 

221.79 

83.92 

12  

0  832 

0  888 

15  09 

4 

148.12 

153.93 

219.65 

83  38 

11  
10  
9  

27  

0.832 
0.832 
0.832 

0  684 

0.881 

0.874 
0.847 

0.766 

15.16 
15.21 
15.32 

15.19 

4 
4 
4 

3 

151.25 
155.00 
160.50 

112.67 

153.12 
152  15 
148.02 

133.24 

214  01 
208.77 
196.52 

183.94 

81.29 
79.55 
76.42 

80.14 

26  
25...  

0.684 
0  684 

0.769 
0.768 

15.12 
15.11 

3 
4 

121  33 

127.67 

133.52 
133.24 

189.83 
191.06 

82.91 
83  6S 

24  
23  
22     

0.684 
0.684 
0.684 

0.762 
0.756 
0.745 

15.14 
15.20 
15.28 

4 
4 
4 

131.50 
135.50 
133  00 

132.34 
131.58 
130.06 

187  85 
185.27 
182  49 

82.67 
81.68 
80.97 

21  
20  
19  

57  .. 

0.684 
0.684 
0.684 

0.568 

0.732 

0.728 
0.719 

0.641 

15.33 
15.39 
15.43 

15.85 

4 
4 
4 

5 

141.75 
147.00 
156.00 

125.80 

128.02 
127.52 
125.  b9 

113.89 

178.39 
176.99 
169.79 

162.59 

80.15 
79.52 
77.01 

79.42 

58  
59  

0.568 
0.568 

0.633 
0.630 

15.88 
15  85 

4 
4 

131.50 
135.75 

112.65 
112.04 

162.80 
160.68 

HO.  25 
79  78 

60     

0  568 

0.629 

15.83 

4 

139  75 

111.68 

157.81 

78  71 

61  
62  

0.568 
0  568 

0.622 
0.613 

15.84 
15.85 

4 
4 

143.25 
148.25 

110.45 
109.02 

152.99 
146.23 

77.11 
74  62 

46 

0  424 

0.500 

16.50 

4 

112.50 

90  70 

123  97 

73  05 

45  

0  424 

0.499 

16.53 

4 

121.25 

90.59 

127.84 

75.28 

47     

0  424 

0.499 

16.49 

4 

124.00 

9U.37 

127.79 

75  61 

44  
49  

0.424 
0  424 

0.497 
0  497 

16.55 
16.47 

4 

4 

127  00 
126  >7 

90.24 
90.04 

127.86 
127.73 

75.49 
75  95 

43        

0  424 

0.494 

16.55 

4 

131.75 

89.69 

125.47 

74  53 

48  
4' 

0.424 
0  424 

0.487 
0.479 

16.50 
16.58 

4 

4 

135.50 
151  25 

88.24 
87  01 

121.67 
113  ig 

73.69 
69  18 

Turbine  Test  Data. 


TABLE  LXVIII. 

Test  of  a  44-inch  Left  Hand  Improved  New  American  Turbine.  Built  by  the 
Dayton  Globe  Iron  Works  Co.,  Dayton,  Ohio.  Testing  Flume  of  the  Holyoke 
Water  Power  Co.  Test.  No.  1609.  March  21,  1904.  Tested  on  Long  Conical 
Draft  Tube.  Balanced  Gate. 

With  the  flume  empty  a  strain  of  7  Ibs.  applied  3.5  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  -wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part.) 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

« 

3 

4 

5 

6 

7 

8 

9 

8  .. 

1.000 
1.000 
.000 
.000 
.000 
.000 
.000 
.000 
.000 
.000 

0.907 
0.907 
0.907 
0.907 
0.907 
0.907 

0.823 
0.823 
0.823 
0.823 
0.823 
0.823 
0.823 
0  823 
0.823 
0.823 
0.823 

0.684 
0.684 
0.6«4 
0.684 
0.684 
0.684 
0.684 
0.684 
0.684 

0.581 
0.581 
0.581 
0.581 
0.581 
0.581 
0.581 

0.459 
0.459 
0.459 
0.459 

0.4.7.t 
0.459 

0.986 
0.988 
0.992 
1.001 
1.014 
1.011 
0.999 
0.98H 
0.976 
0.772 

0.944 
0.948 
0.949 
0.952 
0.945 
0.935 

0.878 
0.882 
0.884 
0.830 
0.871 
0.863 
0.855 
0.848 
0.838 
0.821 
0.796 

0.729 
0.739 
0.746 
0.741 
0.736 
0.725 
0.70.5 
C.6K) 
0.66v> 

0.628 
0.633 
0.633 
0.614 
0.58ti 
0.566 
0.551 

0.496 
0.493 
0.488 
0.468 
0.4.50 
0.441 

15.31 
15.24 
15.23 
15.22 
15.19 
15.18 
15.23 
15.32 
15.37 
16.15 

15.42 
15.42 
15.42 
15.39 
15.47 
15.52 

15.61 
13.59 
13.56 
15.57 
15.61 
15.67 
15.79 
15.75 
15.74 
15.82 
15.94 

16.31 
16.24 
16.19 
16.19 
16.16 
16.17 
16.24 
16.35 
16.41 

16,54 
16.55 
16.56 
16.63 
16.75 
16.87 
16.97 

17.02 
17.03 
17.04 
17.10 
17.11 
17.08 

4 
4 
4 
4 
4 
4 
4 
4 
5 
4 

4 
4 
4 

4 
4 
4 

4 
5 
4 
4 
4 
4 
4 
4 
4 
4 
4 

3 
4 
4 
4 
4 
4 
4 
4 
4 

4 
4 
4 
4 
4 
4 
4 

4 

4 
4 
4 
4 
4 

132.25 
137.75 
141.75 
146.50 
150.50 
155.00 
159.00 
161.75 
165.40 
210.25 

'131.50 
136.00 
139.00 
143.50 
147.75 
151.00 

115.75 
121.00 
131.00 
135.25 
138.50 
142.50 
147.50 
151.50 
156.75 
161.00 
164.00 

98.00 
109.00 
117.75 
122.75 
125.50 
132.00 
139.25 
145.00 
151.50 

108.50 
112.00 
114.50 
124.25 
134.50 
145.00 
156.25 

99.75 
107.25 
112.50 
128.75 
143.00 
152.00 

172.28 
172.13 
172.89 
174.40 
176.35 
175.81 
174.09 
172  57 
170.73 
138.47 

165.47 
166.15 
166.27 
166.  70 
165.87 
164.50 

154.80 
155.32 
155.60 
155.05 
153.55 
152.60 
151.67 
150.20 
146.45 
145.80 
141.85 

131.50 
132.91 
134.05 
133.15 
132.00 
130.22 
126.92 
122.77 
119.79 

114.06 
115.00 
114.90 
111.84 
107.13 
103.84 
101  26 

91.31 
90.75 
89.87 
86.39 
82.01 
81.30 

228.61 
231.64 
233.60 
236.50 
237.89 
234.58 
2<J4.59 
217.59 
205.82 

76.43 

77.86 
78.22 
78.56 
78.31 
77.50 

72'.  57 
69.16 

7  
9  

6  

10  
5  

4  

3  
2  

1  

49... 

231.74 
235.10 
235.61 
236.48 
.233.54 
228.52 

218.00 
225.20 
229.10 
227.43 
223.58 
220.45 
216.28 
208.90 
200.32 
189.51 
176.50 

174.68 
190.62 
201.96 
202.28 
199.95 
195.33 
187.33 
175.56 
163.04 

160.12 
169.50 
169.43 
167.15 
158.32 
146.30 
131.37 

127.  48 
129.85 
128.64 
125  57 
115.43 
102.24 

80.08 
80.91 
81.03 
81.28 
80.25 
78.92 

79.55 

82.06 
83.44 
83.07 
82.25 
81.29 
79.63 
77.86 
75.60 
72.45 
68.83 

71.82 
77.87 
82.05 
82.74 
82.65 
81.80 
80.14 
77.12 
73.14 

74.84 
7«.53 
78.52 
79.24 
77.80 
73.64 
67.41 

72.33 
74.09 
74.07 
74.95 
71.66 
64  92 

48  
47  
46 

45  

44  
21  

j>0  

19 

18  

17.   ..   . 

16 

15  

14     ... 

13 

12  

11  
29... 

30  

28 

S>7  

26  
25 

24  

23... 

22 

36  

37  

35  
34 

33  

32  

31.   . 

43  
42  

41  

40     ... 

39 

38 

Victor  Turbine. 


715 


TABLE  LXIX. 

Test  of  a  43-inch  Right  Hand   Victor   Turbine.    Built  by  the  Plat  Iron  Works 

Co.,  Dayton,  Ohio.     Testing  Flume  of  the  Holyoke  Water  Power  Co.     Test 

No.  1707.     Tested  on   Conical  Draft  Tube.    Swing  Gate.    Nov.  20,  1907. 

With  the  flume  empty  a  strain  of  20  Ibs.  applied  3.6  feet  from  the  center  of  the  shaft, 

sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  pate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

3 

3 

4 

6 

6 

7 

8 

9 

1  

1.000 

0.852 

16  19 

3 

Still 

154  79 

15  

1  000 

0  946 

15  98 

2 

100  00 

170  72 

203  27 

65  69 

14 

1  000 

0  969 

15  93 

H 

122  00 

174  gg 

i!31  46 

73  35 

13 

1  000 

0  985 

15  79 

3 

143  00 

176  80 

247  08 

78  03 

11  

1  000 

0  989 

15  75 

3 

151  33 

177  23 

251  22 

79  35 

10 

1  000 

0  9^8 

15  74 

3 

159  67 

178  78 

254  24 

79  66 

12  

000 

1  002 

15  70 

3 

165  00 

179  22 

254  91 

79  87 

9  

g 

.000 
000 

1.006 
1  005 

15.82 
15  86 

4 
4 

172.25 

178  75 

180.64 
180  79 

256.77 
954  35 

79.22 
78  21 

7  

000 

0  979 

16  01 

4 

178  75 

176  80 

''36  18 

73  57 

6  
5  

.001) 
000 

0.956 
0  93-1 

16.10 
16  23 

4 
3 

183.25 
189  67 

173.26 
169  33 

217  29 
192  77 

68.68 
61  85 

4  
3  

.000 
000 

0.878 
0  808 

16.39 
16  60 

3 
4 

202.67 
214  25 

160.52 
148  59 

137.33 
72  59 

46.02 
25  95 

2  

.000 

0.762 

16.67 

3 

224.00 

140  43 

28  
27  
26  

0.900 
0.900 
0  900 

0.874 
0.901 
0  908 

15.98 
15.93 
15  90 

4 
4 
4 

89.75 
111.75 
127  00 

157.76 
162.30 
163  54 

182.44 
215.80 
232  34 

63.80 
73.59 

78  78 

25.            .   . 

0  900 

0  911 

15  84 

4 

138  50 

163  67 

239  SO 

81  38 

24 

0  900 

0  918 

15  81 

4 

150  °5 

164  76 

244  34 

82  70 

23  

0  UOO 

0  915 

15  81 

4 

158  50 

164  22 

241  64 

82  06 

22  
21  

0.900 
0  900 

0.894 
0  877 

15.88 
15  94 

4 
4 

160.25 
164  00 

160.79 
158  15 

228.02 
216  69 

78.74 
75  79 

20.. 

0  900 

0  862 

15  94 

4 

168  50 

155  31 

205  51 

73  19 

19  

0  900 

0  839 

16  02 

4 

174  00 

151  68 

188  64 

68  45 

18  

0  900 

0  798 

16  21 

4 

184  25 

145  14 

156  OD 

58  48 

16.......... 

0.900 
0  900 

0.743 
0  690 

16.38 
16  59 

3 
2 

199.00 
218  50 

135.86 
126  81 

101.13 

40.07 

38 

0  800 

0  783 

16  32 

3 

60  33 

142  88 

130  34 

49  98 

37  

0  800 

0  837 

16  15 

119  25 

151  91 

218  16 

78  40 

36  
35  

0.800 
0  800 

0.847 
0  847 

16.14 
16  13 

135.50 
146  00 

153  56 
153  56 

234.12 
237  42 

as.  29 

84  51 

34  
33  

0.800 
0  800 

0.824 
0  807 

16.23 
16.  bO 

148.00 
151  75 

149.80 
147  12 

225.63 
215  93 

81.82 
79  39 

32  

0  S(  0 

0  773 

16  42 

161  50 

141  45 

196  97 

74  77 

31 

0  800 

0  726 

16  56 

173  75 

133  30 

164  82 

65  83 

30  

0  800 

0  690 

16  67' 

4 

187  00 

127  18 

126  71 

5''  69 

29  

0  800 

0  627 

16.86 

3 

215  00 

116  21 

47... 

0  700 

0  717 

16  57 

3 

89  33 

131  75 

157  37 

63  56 

48  
46  
45  

0.700 
0.700 
0  700 

0.738 
0.754 
0  752 

16.51 
16.42 
16  38 

R 

3 
8 

110.67 
126.00 
133  00 

135.45 
137.95 
137  41 

189.72 
209.17 
21  1  78 

74.80 
81.42 
82  96 

44  
43  
42  
41  
40  

0.700 
0.700 
0.700 
0.700 
0  700 

0.732 
0.708 
0.678 
0.650 
0  618 

16.44 
16.53 
16.63 
16.70 
16  82 

8 

4 
4 
4 
4 

136.00 
142.25 
150.50 
160.00 
179  50 

133.93 
129.98 
124.90 
120.02 
114  42 

203.73 
192.77 
178.46 
162.62 
121  63 

81.18 
79.10 
75.75 
71.53 
55  72 

39  

0  700 

0.568 

17.02 

3 

209  00 

105  73 

58  

0  600 

0  623 

16  94 

3 

94  67 

115  74 

147  54 

66  35 

57  

56 

0.600 
0  600 

0.634 
0  643 

16.89 
16  83 

3 
3 

105.00 
116  00 

117.55 
119  02 

169.08 
172  Q2 

71.09 
7fi  11 

55  

0  HOO 

0  645 

16  80 

4 

122  50 

119  28 

178  46 

78  52 

54  
53 

0.600 
0  600 

0.625 
0  601 

16.81 
16  90 

4 
4 

126.50 
134  'iO 

115.74 
111  4T 

171.43 

77.66 

52  

0  600 

0  582 

16  97 

4 

144  °5 

108  20 

]56  38 

75  09 

51  

50 

0.600 
0  600 

O.fi60 
0  543 

17.04 
17  14 

4 
4 

160.25 

182  50 

104.44 

135.73 
qo  74 

67.23 

49  

o.'eoo 

0.501 

17.28 

3 

204'  00 

94.03 

Turbine  Test  Data. 


TABLE  LXIX.- Continued. 

Test  of  a  42-inch  Right  Hand  Victor  Turbine.  Built  by  the  Plait  Iron  Works 
Co.,  Dai/ton,  Ohio.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  Test 
No.  1707.  Nov.  20,  1907.  Tested  on  Conical  Draft  Tube.  Siving  Gate. 

With  the  flume  empty  a  strain  of  20  Ibs.  applied  3.6  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
'    feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

67 

0  500 

0  542 

17  32 

3 

94  33 

101  82 

132  31 

66  15 

66  
65  
64  

0.500 
0  500 
0.500 

0.553 
0.556 
0.539 

17.24 
17.19 
17.25 

3 
4 
3 

106.67 
116.35 
122.00 

103.59 
104.06 
101.02 

144.56 
149.66 
144  66 

71.37 
73.77 
73  19 

63  
62. 

0.500 
0  500 

0.515 
0  509 

17.28 
17.29 

4 

4 

135.75 
150  50 

96.66 
95  61 

137.97 
127  47 

72.83 
67  99 

61  

0.500 

0.499 

17.31 

4 

163.00 

93.69 

110  45 

60  04 

60  

0  500 

0.476 

17.39 

8 

184  33 

89  63 

62  45 

35  33 

59 

0  5UO 

0  451 

17  50 

3 

198  33 

85  20 

NOTE— For  experiments  2,  16,  29,  39,  49,  59,  Jacket  Loose. 


McCormick  Turbine. 


717 


TABLE  LXX. 

Test  of  a  39-inch  Left   Hand   McCormick  Turbine.     Built  by   the   S.   Morgan 
Smith  Co.,   York,  Penn.     Testing  Flume  of  the  Holyoke  Water  Power  Co* 
Tested  on  Conical  Draft   Tube.     Test   No.  1191.    May  29,  1899. 
With  the  flume  empty  a  strain  of  6  Ibs.  applied  3.2  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

8              .    . 

1  000 

1  009 

15  79 

I 

126  00 

117  83 

177  36 

84  15 

1.000 

1.006 

15  79 

4 

131  75 

117  46 

178.98 

85.19 

6   

1  000 

1  001 

15  82 

4 

138  00 

116  98 

179  84 

85  78 

5  
4  
'6 

1.000 
1.000 
1  000 

0.998 
0.990 
0  977 

15.85 
15.87 
15  91 

4 
4 

143.00 
150.00 
154  60 

116.73 
115.89 
114  53 

179.32 
177.03 
171  06 

85.56 

84.27 
82.87 

2 

1  000 

0  961 

15  96 

4 

160  25 

112  80 

162  53 

79  70 

1  

1  000 

0  945 

15  98 

4 

185  75 

110  99 

152  83 

76  07 

43  

0  796 

0  903 

15  95 

4 

118.25 

105.98 

159.91 

83  51 

42  
41  

0.796 
0.796 

0.8H9 
0.896 

15.97 
15.97 

4 
4 

123.75 
129.25 

105.51 
105.02 

161.27 
162.08 

84.49 
85  31 

40  

0  796 

0  889 

15  99 

4 

133.00 

104  44 

160  24 

84  70 

39 

0  796 

0  882 

15  98 

5 

136  60 

103  62 

157  86 

84  11 

38  

0  796 

0  874 

16  03 

4 

140.50 

102.78 

155.46 

83.29 

37  
36  

0.796 
0  796 

0.864 
0  853 

16.08 
16.06 

4 
4 

145.00 
149.00 

101.72 
100.45 

151.52 
146.54 

81.78 
80.19 

35  

0  796 

0  843 

16.11 

4 

153  25 

9i).4l 

141  30 

77  89 

34  
33  
32  

0.621 
0.621 
0  621 

0.760 
0.754 

0  748 

16.26 
10.29 
16.29 

4 

4 
5 

123.75 
127.25 

130.80 

89.97 
89.41 

88.  '(3 

136.92 
135.32 
133.47 

82.62 
82.02 
81.51 

31.. 

0  621 

0  742 

16  30 

4 

134  00 

87  94 

130.97 

80  66 

30 

0  621 

0  734 

16  34 

4 

138  25 

87  18 

129  17 

80  05 

29  

0  621 

0  728 

16.35 

4 

142.25 

86.51 

126.79 

79.13 

28  
27  

0.621 
0  621 

0.716 
0  703 

16.37 
16.40 

4 

4 

147.75 
156.25 

85.09 
83.65 

122.61 
115.26 

77.70 
74.17 

26...  

0.498 

0  615 

16.55 

3 

115.00 

77.10 

109.57 

75.80 

25  

0  498 

0  640 

16.55 

4 

120.25 

76.47 

110.14 

76.82 

24  
23  

0.498 
0.498 

0.636 
0.63U 

16.55 
16.56 

5 

4 

123.60 
127.75 

7o.95 
75.31 

108.65 
107.58 

76.30 
76.15 

22 

0.498 

0  625 

16.59 

4 

131.75 

74.77 

106.09 

75.50 

21  

0.498 

0.619 

16.60 

4 

136.25 

74.12 

104.69 

75.11 

20  

0  498 

0.611 

16.69 

4 

143.00 

73.30 

101.09 

72.94 

19  
18  

17 

0.498 
0.498 

0  390 

0.600 
0.588 

0  527 

16.71 
16.78 

16  72 

4 
4 

4 

150.25 

157.75 

116.75 

72.03 
70.71 

63.25 

86.13 

87.27. 

83.97 

69.77 
64.93 

70  09 

16  
15 

0.390 
0  390 

0.522 
0.516 

16.73 
16.75 

4 
4 

121.50 
125.50 

62.66 
62.06 

82.90 
81.77 

69.81 
69.44 

14  
13  

0.390 
0.390 

0.512 
0.509 

16.78 
16.77 

4 
4 

129.50 
133.00 

61.66 
61.28 

80.40 

78.48 

68.60 
67.42 

12  

0  390 

0.506 

16.76 

4 

135.50 

60.86 

76.63 

66.32 

11  
10  

0.390 
0  390 

0.502 
0.495 

16.75 
16.77 

4 
4 

139.75 
145.00 

60.38 
59.60 

73.88 
70.41 

64.48 
62.19 

9  

0  390 

0.489 

16.77 

5 

150.60 

58.81 

64  80 

58  00 

7i8 


Turbine  Test  Data. 


TABLE  LXXI. 

Test  of  a  3ff-mch  Right  Hand  Swain  Turbine.  Built  by  the  Swain  Turbine  and 
Mfg.  Co.,  Lowell,  Mass.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  No. 
977.  Date  Jan.  20-21.  1807. 


Number 
of 
experi- 
ment* 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

64  

63 

1.000 
1  000 

1.004 
995 

IS.  16 
15  25 

3 
4 

130.33 
135  00 

76.49 
75  98 

111.57 
111  47 

84  84 
84  83 

62  

1  000 

984 

15  40 

3 

140  83 

75  52 

111  61 

84  62 

61  
60  

1.000 
l.UOO 

.973 
.966 

15.42 
15.43 

3 

4 

144.00 
146.50 

74.74 
74.19 

110.16 
108.51 

84.28 
83  58 

59  

1.000 

954 

15  48 

4 

150  75 

73  45 

107  08 

83  04 

58  
57 

1.000 
1  000 

.945 

934 

15.47 
15  44 

4 
3 

154.00 
158  00 

72.73 

71  7t> 

104.72 
101  68 

82.07 
80  92 

56    

1  000 

922 

15  33 

4 

161  37 

70  58 

97  97 

79  84 

55  
54  

.875 
875 

.932 
925 

15.16 
15  15 

3 
4 

132.00 
135  75 

70.95 
70  42 

102.58 
102  20 

P4.10 

84  47 

53  .. 

875 

916 

15  28 

4 

140  75 

70  01 

102  54 

84  52 

52  
51  

.875 

875 

.907 
896 

15.41 
15  50 

4 

4 

147.00 
153  50 

69.61 
68  99 

102.63 
101  58 

84.37 
83  75 

50  
49  

.875 
750 

.877 
866 

15.60 
15  66 

3 

4 

162.33 
130  00 

67.75 
67  03 

98.55 
100  24 

82.22 
84  20 

48  

750 

857 

15  74 

4 

136  00 

66  52 

100  73 

84  83 

47  
46  

.750 
750 

.849 
844 

15.76 
15  70 

4 
2 

141.00 
146  00 

65.96 
65  41 

100.16 
99  28 

84.96 
85  24 

45  
44  
43  

.750 
.750 
750 

.838 
.829 
826 

15.54 
15.62 
15  16 

4 
3 
4 

149.75 
157.33 
156  75 

64.64 
64.09 
62  88 

97.28 
96.47 
91  36 

85.39 

84.97 
84  51 

42  

750 

814 

15  20 

4 

162  75 

6;i  06 

88  ^3 

83  13 

41 

625 

783 

15  30 

127  50 

59  90 

85  Q2 

82  «7 

40  

625 

775 

15  38 

4 

134  75 

59  45 

86  72 

83  63 

3tt  
38  

.625 
625 

.767 

758 

15.43 
15  47 

4 
4. 

142.12 
149  50 

58.95 
58  30 

87.15 
86  23 

84.48 
84  30 

37  

625 

749 

15  51 

4 

154  50 

57  70 

84  42 

83  18 

36. 

625 

733 

15  58 

4 

162*75 

56  62 

81  02 

80  99 

35 

625 

715 

"15  K5 

IRQ  -Vl 

55  32 

7fi  TS 

77  cc 

34.. 

500 

683 

15  74 

123  20 

52  93 

74  PO 

79  09 

33 

500 

676 

15  78 

1  m  2^ 

59  54 

75  70 

XO  ^1 

32  
31  
30 

.500 
.500 
500 

.668 
.660 
652 

15.83 
15.85 

1  C01 

4 

4 

137.50 
144.00 

ICf)    OC 

51.98 
51.42 

50  87 

75.13 
74.31 
72  98 

80.51 
80.40 
79  ^,1 

29  

28 

.50J 
500 

.644 
635 

15.95 
15  96 

4 

157.50 
163  33 

50.31 
49  6'-* 

71.72 
69  41 

78.81 
71*  oq 

26 

375 

CR7 

-ion   07 

4.2  50 

T.4  08 

70  7- 

25  
24. 

.375 
375 

.552 
545 

15.19 

IK    O1 

4 

127.50 
•>oq  cr» 

42.06 
41  58 

54.19 

CO    AG 

74.78 

74.  *S8 

23  

375 

538 

15  °1 

4 

130  00 

41  06 

5>>  33 

73  87 

22  
21. 

.375 
375 

.531 
*>24 

15.22 

3 

145.67 

40.53 

51.30 
49  94 

73.32 
70  qc 

20  
27  

.375 
375 

.514 
504 

15.30 

1C    Of) 

4 

160.25 
167  20 

39.36 
38  57 

48.65 
45  68 

71.23 
68  25 

19     
18  

.250 
250 

.420 
416 

15.53 
15  54 

113.50 
120  25 

32.40 
3''  11 

36.52 
36  50 

64.00 
64  50 

17  

250 

412 

ic   C7 

noc  en 

qi     QQ 

36  10 

64  22 

16... 

250 

407 

01     AR 

35  60 

cq   qi 

15  

250 

401 

15  60 

1^9  50 

'31    00 

34  72 

63  31 

14  
13  
12.. 

.250 
.250 
250 

.396 
.386 

378 

15  61 
15  66 

146.25 
155.75 

30.59 
29.91 

33.74 
32.15 

on  7u 

62.31 
60.52 

11. 

250 

qfi7 

10... 

.250 

•AZK 

1*  70 

A 

170    KH 

97  KA_ 

91    KO 

J.J   fU 

Swain  Turbine. 


719 


TABLE  LXXL— Continued. 

Test  of  a  36-inch  Right  Hand  Swain  Turbine.  Built  by  the  Swain  Turbine  and 
Mfg.  Co.,  Lowell,  Mass.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  No. 
977.  Date  Jan.  20-21,  1897. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part) 

Proportional 
discharge 
(discharge 
at  full  gate 
with  hignest 
efficiency  =1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

9 

0  125 

0  257 

16  03 

4 

111  50 

20  06 

16  92 

46  41 

8  

125 

254 

16  01 

4 

119  00 

19  89 

16  62 

46  01 

7 

125 

252 

16  07 

4 

126  75 

19  76 

16  16 

44  88 

6  

125 

249 

16  17 

4 

134  12 

19  62 

15  47 

43  00 

125 

247 

16  23 

4 

141  00 

19  45 

14  55 

40  65 

4  

135 

245 

16  18 

4 

146  25 

19  24 

13  32 

37  73 

3...,  

.125 
125 

.242 
239 

16.22 
16  11 

4 
4 

152.25 
159  50 

19.07 
18  73 

12.02 
9  68 

34.26 
28  30 

1  . 

067 

161 

16  49 

4 

153  25 

12  80 

720 


Turbine  Test  Data. 


TABLE  LXXII. 

Test  of  a  36-inch  Eight  Hand  Victor  Turbine.     Built  by  the  Platt  Iron  Works 
Co.,  Dayton,  Ohio.     Testing  Flume  of  the  Holyoke  Water  Power  Co.     Test 
No.  1061,  December  14,  1897.     Tested  on  Conical  Draft  Tube.     Cylinder  Gate. 
With  the  flume  empty  a  strain  of  8  Ibs,  applied  3.2  feet  from  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

» 

12  
11  
10  

1.000 
1.000 
1.000 

1.010 
1.009 
1.009 

16.75 
16.76 
16.74 

3 
4 
4 

133.33 
139.25 
144.87 

116.38 
116.38 
116.27 

175.20 
176.99 
177.91 

79.24 

80.01 
80  59 

9  

1  000 

1  002 

16  79 

4 

150  75 

115  63 

177  73 

80  71 

8  

6 

1.000 

ooo 

0.997 
0  992 

16.80 
16  73 

4 

4 

155.00 
156  50 

115.04 
114  30 

176.07 
172  97 

80.33 
79  75 

5.'.'.'.  .'..'.'.. 
4  

.'ooo 

.000 
.000 

0.982 
0.975 
0  965 

16.82 
16.69 
16.58 

4 
4 
4 

161.75 
162.75 
167.00 

113.46 
112.21 
110  63 

173.81 
169.89 
164  07 

80.30 
79.98 
78  87 

3           

000 

0  953 

16  59 

4 

172  25 

109  31 

158  65 

77  14 

2  
1  
53  

.000 
.000 
.000 

0.941 
0.923 
0.748 

16.65 
16.70 
17.33 

4 
4 

4 

177.25 
184.00 
240.50 

108.09 
106.21 
87  70 

152.37 
141.23 

74.65 
70.20 

52  

0.900 

0  967 

16  92 

4 

133  75 

112  07 

172  47 

80  19 

51  
50  
49  

0.900 
0.900 
0.900 

0.965 
0.959 
0  953 

16.99 
17.01 
17  04 

4 
4 
4 

139.50 
144.00 
148  50 

112.07 
111.37 
110  76 

174.74 
174.19 
173  25 

80.92 
81.07 
80  93 

48  
47  
46  

0.900 
0.900 
0.900 

0.947 
0.939 
0  925 

17.03 
17.04 
17  05 

4 
4 
4 

152.00 
157.00 
164  00 

110  03 
108.19 
107  62 

"   171.73 
170.63 

168  17 

80.81 
80.86 
80  81 

45  

0  900 

0  914 

17  06 

2 

170  00 

106  32 

161  80 

78  65 

44  

0.801 

0  900 

17  10 

3 

132  33 

104  79 

160  07 

78  76 

&  
42  
41  

0.801 
0.801 
0  801 

0.900 
0.899 
0  892 

17.07 
17.02 
17  02 

4 
4 
4 

137.75 
142.25 
147  00 

104.67 
104.32 
103  61 

162.40 
162.46 
161  57 

80.14 
80.64 

80  78 

40  

0  801 

0  884 

17  02 

4 

151  25 

102  68 

159  74 

80  59 

39  
38  

0.801 
0.801 

0.870 
0  863 

17.02 
16  97 

4 
4 

155.25 
159  25 

101.04 
100  09 

157.29 
154  50 

80.64 
80  'J0 

37  

0  80  I 

0  816 

16  92 

4 

163  50 

99  18 

150  59 

79  1  ° 

36  

35... 
34..     .   . 

0.801 

0.701 
0  701 

0.845 

0.814 
0  814 

16.89 

16.89 
16  90 

4 

3 
4 

168.25 

125.67 
133  25 

97.79 

94.25 
94  25 

144.64 

134.27 
139  09 

77.21 

74.37 
76  99 

33  

0.701 

0  812 

16  89 

4 

138  75 

94  03 

140  58 

78  04 

32  

0  701 

0  807 

16  92 

4 

144  25 

93  47 

140  83 

78  51 

31     

0  701 

0  7'94 

17  00 

92  20 

130  75 

78  61 

30.  
29  

0.701 
0  701 

0.787 
0  776 

17.07 
17  15 

5 

153.60 
158  75 

91.54 

90  52 

137.70 
134  52 

77.70 
76  40 

28  

0.701 
0  601 

0.768 
0  717 

17.15 
17  24 

4 
4 

163.25 
129  00 

89.52 
83  87 

130.31 
117  23 

74.84 
71  49 

26  

0  601 

0  714 

17  29 

137  00 

CO   ce 

120  29 

73  33 

25. 

0  601 

0  705 

17  36 

oo  77 

73  04 

24  

0  601 

0  6% 

17  41 

4 

148  00 

81  91 

119  05 

73  48 

23  

0  601 

0  685 

17  47 

CM   (•.) 

116  12 

7°  69 

22  
21 

0.601 
0  601 

0.676 

17.53 

4 

159.00 

79.77 

112.28 

70.79 
fi8  3Q 

20  

0  502 

0  622 

17  60 

1OO     00 

96  93 

66  00 

19  
18  

0.502 
0  502 

0.617 
0  609 

17.55 
17  55 

3 
3 

131.07 
138  00 

72.85 
71  81 

98.64 
98  29 

68.02 

68  77 

17  

0  502 

0  598 

17  56 

3 

W'V? 

68  41 

10  

0  502 

0  592 

17  55 

fiQ  87 

OQ    1Q 

15  
14  

0.502 
0  502 

0.588 
0  580 

17.56 
17  56 

4 
3 

155.37 

IpO     RA 

69.34 

90.63 
85  34 

65.63 
62  61 

13  

0  502 

0  573 

17  55 

fi7  R1 

78  4O 

58  26 

For  experiment  53,  the  jacket  was  removed  from  the  dynamometer. 


Special  Smith  Turbine. 


721 


TABLE  LXXIII. 

Test  of  a  33-inch  Special  Left  Hand  Turbine.  Built  by  the  S.  Morgan  Smith 
Co.,  York.  Penn.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  Test 
No.  1511.  March  25  and  26,  1904.  Tested  on  Conical  Draft  Tube.  Bal- 
anced Gate. 

With  the  flume  empty  a  strain  of  9  Ibs.  applied  3.3  feet  from  the  center,  sufficedto  start  the  wheel 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part. 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency=l). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

15  

1  000 

0  995 

17  01 

4 

196  00 

112  81 

178  22 

81   s'( 

14  
13  

1.000 
1  000 

0.998 
1  000 

16.99 
16  98 

5 
4 

203.80 
208  75 

113.05 
113  20 

178.92 
179  34 

82.14 

GO    97 

12  

1  000 

1  003 

16  99 

4 

21'i  50 

113  55 

179  40 

09  nn 

11  
10  

1.000 
1  000 

1.004 
0  995 

16.95 
16  94 

4 
4 

220.00 
221  50 

113.55 
112  5" 

177.97 
173  62 

81.53 

Of)    00 

9  

1.000 
0  948 

0.984 
0  964 

17.00 
17  05 

4 
4 

223.50 
194  75 

111.46 
109  42 

168.18 
mOK 

78.27 

GO  7/) 

5  
6  

0.948 
0  948 

0.967 
0  969 

,     17.11 
17  08 

4 
4 

201.50 
204  75 

109.90 
110  02 

179.43 
179  75 

84.13 

QA     QK 

4 

0  948 

0  968 

17  14 

4 

209  75 

110  14 

ISO  20 

84.   17 

3  

0  948 

0  959 

17  19 

4 

211  75 

109  30 

175  ''8 

82  26 

2  

0  948 

0  952 

17  17 

4 

913  00 

108  45 

170  97 

on   QA 

1 

0  948 

0  949 

17  19 

4 

214.  7*1 

-inu  11 

ICQ     00 

8  

0  948 

0  939 

17  09 

5 

216  40 

106  69 

162  84 

78  7^ 

71  
70  

0.883 
0  883 

0.909 
0  910 

17.29 
17  25 

4 

4 

181.75 
185  75 

103.84 
103  84 

173.24 
173  56 

85.08 
ftS  44 

69 

0  883 

0  914 

17  93 

4 

193  00 

104  20 

17^  4Q 

0(1     1Q 

68  

0  883 

0  909 

17  24 

4 

197  00 

103  71 

172  95 

85  29 

67  
66  

0.883 
0  883 

0.901  . 
0  893 

17.28 
17  31 

4 
5 

199.25 
202  00 

102.90 
102  09 

168.68 
164  67 

83.65 
82  17 

64 

0  883 

0  876 

17  36 

4 

208  50 

100  34 

iKt;  on 

7Q  42 

54... 

0  851 

0  894 

17  15 

4 

191  00 

101  72 

170  08 

OK  Q7 

53 

0  851 

0  883 

17  19 

4 

193  50 

100  58 

166  24 

Q4    ITU 

52  

0  851 

0  875 

17  20 

4 

196  50 

99  77 

162  65 

83  58 

51  

0  851 

0  868 

17  27 

4 

200  25 

99  07 

159  48 

82  19 

50 

0  851 

0  858 

17  29 

4 

203  25 

98  02 

IKK   KA 

of)  qr\ 

49  

0  851 

0  851 

17  32 

4 

20(5  25 

97  35 

152  62 

79  81 

48  
47  

0.851 
0  851 

0.842 
0  836 

17.38 
17  37 

4 
4 

210.25 
212  67 

96.50 
95  74 

150.30 
146  70 

79  02 

77  78 

46     .... 

0  851 

0  827 

17  42 

4 

215  50 

94  82 

141  90 

75  75 

45  

0.851 

0  813 

17  44 

4 

218  25 

93  34 

136  86 

74  13 

44  
43  

0.765 
0  765 

0.836 
0  823 

17.37 
17  38 

4 
4 

169.25 
172  75 

95.73 
94  25 

161.32 
160  33 

85.55 
86  30 

42     

0  765 

0  818 

17  41 

5 

177  60 

93  79 

159  26 

86  00 

41  

0.765 

0  803 

17  45 

4 

181  75 

92  2o 

153  86 

84  33 

40  

0  765 

0  778 

17  48 

4 

192  75 

89  41 

145  04 

81  83 

39  
63  

0.765 
0  702 

0.736 
0  764 

17.55 
17  33 

4 
3 

206.25 
159  00 

84.77 
87  39 

129.34 
144  57 

76.66 
84  17 

62 

0  702 

0  765 

17  33 

3 

166  67 

87  50 

147  37 

85  69 

61  ,  

0  702 

0  763 

17  35 

4 

168  50 

87  28 

145  82 

84  91 

60  

0  702 

0  750 

17  37 

3 

172  00 

85  95 

143  45 

84  73 

59  
58  

0.702 
0  702 

0.739 
0  729 

17.38 
17  42 

3 
4 

175.67 
180  25 

84.66 
83  56 

139.90 
136  77 

83.84 

82  85 

57  

0  702 

0  720 

17  44 

4 

185  00 

82  57 

133  41 

81  69 

56  
55  

0.702 
0  702 

0.707 
0  690 

17.48 
17  50 

4 
4 

189.00 
197  75 

81.18 
79  34 

130.37 
124  01 

81.01 

78  75 

31  

30 

0.636 
0  636 

0.711 
0  705 

17.71 
17  69 

4 
4 

162.50 
166  25 

82.24 
81  51 

137.57 
135  53 

83.28 

82  Kft 

29  

0  636 

0  696 

17  71 

4 

170  50 

80  43 

133  65 

82  73 

28  

0  636 

0  689 

17  69 

4 

173  58 

79  58 

131  65 

82  46 

27  
26  

0.636 
0  636 

0.680 
0  670 

17.70 

17  72 

4 
4 

176.50 
180  25 

78.60 
77  54 

129.50 
126  60 

82.08 
81  24 

25  

0  636 

0  658 

17  74 

4 

187  50 

76  15 

123  46 

80  58 

24  

0.636 

0!659 

17!  73 

4 

209.50 

76^28 

118.24 

77.09 

44 


722 


Turbine  Test  Data. 


TABLE  LXXIIL— Continued. 

Test  of  a  33-inch  Special  Left  Hand  Turbine.  Built  by  the  S.  Morgan  Smith 
Co.,  York,  Penn.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  Test 
No.  1511.  March  25  and  26,  190 1*.  Tested  on  Conical  Draft  Tube  Bal- 
anced Gate. 

With  the  flume  empty  a  strain  of  9  Ibs.  applied  3.3  feet  from  the  center,  sufficed 
to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part. 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

22           

0  556 

0  616 

17  77 

4 

126  25 

71  40 

102  92 

71  53 

23  
21  

0.556 
0  556 

0.638 
0  632 

17.75 

17  74 

5 
4 

153.00 
156  00 

73.82 
73  20 

120.89 
119  35 

81.  35 
81  04 

20  

0  556 

0  619 

17  78 

4 

161  00 

71  73 

116  10 

80  27 

19  
18  

0.556 
0  556 

0.605 
0  589 

17.79 
17  80 

4 
4 

184.50 
205  75 

70.10 
68  33 

109.91 
103  °2 

77.71 

74  83 

17  

0  556 

0  564 

17  83 

4 

^35  00 

65  4-> 

73  68 

55  70 

Victor  Turbine. 


723 


TABLE  LXXIV. 

Test  of  a  33-inch  Right  Hand  Victor  Turbine.  Built  by  the  Platt  Iron  Works 
Co.,  Dayton,  Ohio.  Testing  Flume  of  the  Holyoke  Water  Power  Co.  Test 
No.  1250,  May  29  and  31,  1900.  Tested  on  Conical  Cylinder,  Wicket  or  Swing 
Gate. 

With  the  flume  empty  a  strain  of  12  Ibs.  applied  3.2  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 
(propor 
tional 
part). 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

6          

1  000 

0  998 

16  95 

4 

156  50 

114  36 

146  64 

66  76 

1  000 

0  999 

16  99 

4 

161  25 

114  61 

148  13 

67  13 

5  

1  000 

1  001 

16  96 

4 

163  00 

114  74 

147  74 

67  00 

4 

1  000 

1  002 

16  95 

4 

169  37 

114  86 

147  29 

66  77 

;{  

i  oon 

1  004 

16  93 

4 

174.25 

114  99 

146  20 

66  27 

2 

1  000 

1  005 

16  93 

4 

181  50 

115  11 

144  50 

65  44 

1 

1  000 

1  Oj6 

16  98 

5 

191  20 

1  15  34 

140  51 

63  32 

19  
18  

0.878 
0  878 

0.977 
980 

16.96 
16.93 

4 
4 

155.75 
160.87 

112.02 
112  27 

150.71 
151  72 

70.01 
70  44 

17            

0  878 

981 

16  95 

5 

167  00 

112  40 

152  39 

70  59 

16  

0  878 

983 

16.94 

4 

173.00 

112  63 

15150 

70  08 

15  

0  878 

982 

16.98 

5 

101.20 

112  63 

149  81 

69  10 

24... 
23 

0.785 
II  785 

.937 

938 

.02 
03 

5 
4 

159.20 
163.25 

107.56 
107  70 

155.99 
155  96 

75.20 
75  04 

22  

0  7H5 

936 

.08 

4 

169.75 

107  70 

156  9« 

75  31 

''1 

0  78o 

935 

.07 

4 

177.75 

107  56 

156  75 

75  35 

20  

0  785 

935 

.06 

4 

191.25 

107.44 

152.26 

73  31 

30  
29  

0.688 
0  688 

.872 
872 

.15 
.15 

3 
5 

162.00 
167.00 

100.51 
100.51 

154.77 
155  46 

79.24 
79  59 

28  
X7  

0.688 
0  6^8 

.870 

867 

.16 

.18 

4 
4 

171.50 
175.50 

100.27 
100.04 

155.44 
154.77 

79.73 

79.47 

26     

0  688 

863 

.20 

4 

181.00 

99  57 

152  97 

78  83 

25  

0  688 

858 

.22 

4 

187.75 

98.53 

149  47 

77.75 

38  
37  

0.595 
0  595 

.796 
793 

.53 
.50 

4 
4 

152.75 
158.50 

92.81 
92.35 

147  80 
148.51 

80.17 
81.10 

36 

0  595 

791 

48 

4 

163.50 

92.02 

148  19 

81  31 

35  
34     

0.595 
0  595 

.784 
779 

.47 
.43 

4 

4 

169.00 
173.50 

91.24 
90.57 

146.97 
145.57 

81.37 
81  38 

33 

0  595 

773 

.39 

4 

178.25 

89.68 

143  00 

80  92 

32  

0  595 

.765 

.38 

4 

181.50 

88.75 

138.94 

79.50 

31  
14 

0.595 
0  472 

.756 
677 

1   .40 
1   .63 

5 

4 

184.60 
148.00 

87.76 
79.15 

135.66 
126.89 

78.40 
80.25 

13 

0  472 

670 

1   .67 

4 

155.25 

78.41 

128  35 

81  76 

12  
11  
10  

0.472 
0.472 
0  472 

.662 
.654 
.646 

1   .69 

1   .68 

5 
4 
4 

160.80 
164.50 
170.00 

77.45 
76.50 
75.64 

128.02 
125.93 
123.89 

82.46 
82.17 
81.71 

9 

0  472 

.639 

1   .68 

4 

177.00 

74.80 

121.40 

81.02 

8 

0  472 

633 

1   .70 

4 

184.00 

74.17 

118.32 

79  54 

51           

0  386 

.555 

1   .92 

4 

150.25 

65.43 

101.22 

76  18 

50  
49  
48     

0.386 
0.386 
0  386 

.548 
.547 
.542 

1   .94 
1    .95 
1     97 

5 
4 

4 

156.40 
161.25 
167.75 

64.63 
64.44 
63.93 

100.57 
99.74 
98.62 

76.55 
76.10 
75  76 

47  

0.386 

.539 

17.97 

4 

175.25 

63.54 

96.59 

74.66 

46  

45  
44     

0.386 

0.304 
0.304 

.531 

.450 
.447 

18.00 

18.17 
18.17 

4 

4 

4 

188.00 

146.25 
151.25 

62.74 

53.41 
53.01 

92.11 

78.82 
77.81 

71.98 

71.68 
71.29 

43  . 

0  304 

.445 

18.14 

4 

156.50 

52.74 

76.67 

70.73 

42  
41  
40 

0.304 
0.304 
(1  304 

.443 
.442 
.439 

18.14 
18.13 
18.15 

4 
4 
4 

162.50 
168.50 
17'6.75 

52.54 
52.  35 

52.10 

75.63 
74.30 
71.44 

70.03 
69.09 
66  67 

39  

0.304 

.435 

18.15 

4 

187.75 

51.63 

66.69 

62.81 

724 


Turbine  Test  Data. 


TABLE  LXXV. 

Test  of  a  30-inch  Special  Chase  Jonval  Turbine.  Built  by  the  Chase  Turbine 
Mfg.  Co.,  Orange,  Mass.  Testing  Flume  of  the  Holyoke  Water  Power  Co. 
No.  256.  June  7,  1884. 

With  the  flume  empty  a  strain  of  4  Ibs.  applied  2.4  feet  from  the  center  of  the  shaft 
sufficed  to  start  the  wheel. 


Number 
of 
experi- 
ment. 

Gate 
opening 

°BSKT 
part. 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =  1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse- 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

B 

1  :.... 
8  
7  
6 

1.000 
1.000 
1.000 
1  000 

0.960 
1.008 
1.004 
1  004 

14.72 
14.51 
14.43 
14  61 

3 
3 
8 

3 

Still. 
169.67 
181.67 
196.33 

39.74 
41.42 
41.16 
41.42 

49.66 
50.68 
52  08 

72.98 
75.36 
76.00 

5 

1  000 

0  998 

14  57 

4 

204  75 

41  1(1 

51.50 

75  96 

4  

1  000 

0  999 

14  41 

3 

215.00 

40.91 

51.13 

76.60 

8  
2  

1.000 
1  000 

1.001 
0  998 

14.41 
14.49 

3 
5 

225.00 
244.  £0 

41.02 
40.99 

^50.42 

50  38 

75.34 
74.91 

22... 

0  930 

0  922 

14  68 

4 

185  75 

38  12 

49.27 

77.76 

21... 

0  930 

0  920 

14.72 

6 

194.17 

38.07 

49.73 

78.37 

23  

0  930 

0  919 

14  78 

4 

203.75 

38.12 

50  32 

78.88 

24  
25  

17... 

0.930 
0.930 

0  837 

0.916 
0.913 

0  831 

14.87 
14.95 

15  28 

4 
4 

3 

213.00 
226.00 

180.00 

38.13 

38.07 

35  07 

50.66 
50.65 

46  10 

78.90 
78.59 

75.98 

16.. 

0  837 

0  827 

15  42 

4 

191  00 

35  03 

47  17 

77.12 

15  

0  837 

0  826 

15  42 

3 

199  67 

35  00 

47.49 

77.71 

18  

0  837 

0  823 

15  33 

3 

207  00 

34  75 

47  34 

78.47 

19  

0  837 

0  822 

15  28 

4 

215  00 

34.65 

47.20 

78.73 

20  

14... 

0.837 
0  674 

0.818 
0  666 

15.26 
16  13 

4 
4 

228.25 
163.50 

34.49 

28.85 

46  98 
35.15 

78.82 
66.70 

13  
12.... 

0.674 
0  674  ' 

0.663 
0  661 

16.14 
16  07 

4 

174.25 

185  33 

28.75 
28.61! 

a=>.86 

36  45 

68.25 
70.04 

11  

6  674 

0  669 

16.11 

4 

195  50 

28.52 

36.66 

70.46 

10  

0  674 

0  655 

16  14 

4 

206  50 

28.40 

36.83 

70.97 

9  

0  67  i 

0  650 

16.20 

4 

217.00 

28.25 

36.72 

70.86 

30... 

'0  488 

0  462 

17  10 

4 

142.25 

20  62 

16.26 

40.74 

29  

0  488 

0  460 

17  11 

4 

158  50 

20  55 

16  67 

41.88 

28  

0  48S 

0  458 

17  08 

3 

174  33 

20.43 

16.74 

42.38 

27  

0  488 

0  459 

17  02 

4 

182  50 

20  43 

16.69 

42.40 

26  

0  !-- 

0   lf>s 

17.07 

3 

190.67 

20.43 

16.57 

41.96 

31     

0  488 

0  457 

17  09 

5 

206  20 

20  37 

10.03 

40.67 

Chase  Jonval  Turbine. 


725 


TABLE  LXXVI. 

Test  of  a  30-inch  Regular  Chase  Jonval  Turbine.  Built  by  the  Chase  Turbine 
Mfg.  Co.,  Orange,  Mass.  Testing  Flume  of  the  Holyoke  Water  Power  Co. 
June  10,  1884. 

With  the  flume  empty  a  strain  of  33  Ibs.  applied  2.4  feet  from  the  center  of  the  shaft, 
sufficed  to  start  the  wheel. 


Xumber 
of 
experi- 
ment. 

Gate 
opening 
(propor- 
tional 
part;  . 

Proportional 
discharge 
(discharge 
at  full  gate 
with  highest 
efficiency  =1). 

Mean 
head  in 
feet. 

Duration 
of  test  in 
minutes. 

Revolu- 
tions per 
minute. 

Dis- 
charge 
in  sec- 
ond- 
feet. 

Horse 
power 
devel- 
oped. 

Percent- 
age of 
effi- 
ciency. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1  

000 

0  938 

15.62 

3 

Still. 

33  33 

6  
5  

.OOU 
000 

0.993 
0  995 

15.32 

15.29 

3 

3 

194.CO 
201.67 

34.93 
34.96 

43.48 
43.35 

71.70 
71.58 

4  

000 

0  996 

15  30 

5 

211  14 

35  00 

43  46 

71  62 

3  

29 

.000 
.000 

0  889 

1.001 
1.007 

0  894 

15.27 
15.26 

15  78 

3 
3 

4 

222.33 
237.00 

174  75 

35.14 
35.34 

31  93 

43.72 
43.36 

41  56 

71.92 
70.96 

72  80 

2S  

0  889 

0  897 

15.77 

4 

190  25 

32  01 

42  64 

74  55 

27  
20  

0.888 
0  889 

0.897 
0.898 

15.75 

15  80 

4 

4 

200.25 
211.25 

32.01 
32.10 

43.05 

43.48 

75.36 
75.66 

23 

0  889 

0  901 

15  77 

3 

220  67 

32.17 

43  40 

75  50 

24  

0.889 

0.903 

15.74 

4 

232.00 

32.20 

43.50 

75.76 

25  

0  889 

0  907 

15.72 

3 

242.67 

32.33 

43  29 

75.17 

22 

0  733 

0.756 

16.30 

4 

184.50 

27.43 

36.28 

71.63 

o* 

0  733 

0.757 

16.24 

4 

195.25 

27.41 

36  61 

72  59 

20  

9.733 

0.75S. 

16.27 

4 

•.'Or.OO 

27.47 

36.92 

72.91 

18  

19 

0.733 
0  733 

0.756 
0  757 

16.28 
16.32 

H 

4 

218.67 
230.50 

27.43 
2i'.47 

37.00 
36.90 

73.14 
72  64 

14  
13  
12  
15 

0.611 
0.611 
O.S11 

0  611 

0.644 
0.644 
0.641 
0.644 

16.65 
16.65 
16.68 
16.77 

5 
4 
3 
3 

175.80 

188.75 
202.00 

209.  as 

23.63 
23.60 
23.54 
23  63 

27.34 
27.62 
27.72 
27  76 

61.33 
62.05 
62.16 
62  21 

]H  

11.811 

0.644 

16.67 

3 

221.33 

23.64 

27.33 

61  21 

17         

0  611 

0.647 

16.61 

3 

236.33 

23.71 

27.02 

60  56 

7 

0  411 

0.469 

17.14 

3 

141  33 

17  47 

12  93 

38  10 

8      

0  411 

0  469 

17.20 

4 

157.00 

17.47 

12.92 

37  96 

LI 

0  411 

0.468 

17.17 

4 

166.00 

17.43 

12  91 

38  06 

]ti  

0.411 

0.469 

17.13 

4 

184.  (HI 

17.43 

12.62 

36.46 

11 

0  411 

0.471 

17.16 

3 

201).  00 

17.53 

11.89 

34  89 

APPENDIX  E. 


EFFECT  OF  AN   "UMBRELLA"    UPON   THE   FORMATION 

OF  VORTICES. 

Report  of  Test  Made  on  30-Inch  Horizontal  Wheel  With  "Umbrella"  at  -the 
Holyoke  Water  Power  Company's  Flume,  April  25th  to  27th,  1907,  by 
F.  Moeller,  Engineer  Power  and  Mining  Department  of  the  Wellman, 
Seaver,  Morgan  Co.  for  The  Southern  Wisconsin  Power  Company. 

The  general  arrangement  of  the  wheel  and  testing  apparatus  is  shown  by 
Fig.  407. 

Before  begin^ng  the  test  it  was  desired  to  note  the  action  of  the  water 
without  umbrella  in  place.  The  penstock  was  filled,  the  level  of  the  water 
being  8'  above  the  center  of  the  shaft,  making  the  total  head  of  water  16.2'. 
Under  this  condition,  with  the  head  stationary  and  the  wicket  gates  wide 
open,  a  large  vortex  was  formed  immediately  above  the  wheel. 


Fig.  407. 


Formation  of  Vortices. 


727 


The  umbrella  which  was  first  made  T  in  diameter  and  dished  11",  was 
lowered  into  the  penstock  until  the  edge  was  3.1'  above  the  center  of  the 
shaft,  with  the  level  of  the  water  the  same  as  before.  With  this  arrangement 
no  vortex  was  formed  immediately  above  the  wheel,  but  there  were  vortices 
near  the  edge  of  the  umbrella,  (see  Fig.  408).  The  umbrella  was  then  re- 
moved and  a  raft  8'  square  was  built  of  matched  pine  about  l1/^"  thick, 
tongued  and  grooved  and  placed  as  nearly  as  possible  over  the  center  of  the 
wheel  on  the  surface  of  the  water.  This  did  not  prevent  the  formation  of 
vortices.  The  raft  was  then  increased  from  8'x8'  to  8'xl2',  and  placed  in  po- 
sition as  shown  in  Figure  409.  This  entirely  prevented  the  formation  of 
vortices  under  the  same  condition  of  head  as  before  and  under  all  the  run- 
ning conditions  of  the  wheel. 

Regarding  these  vortices  it  was  observed  that  all  of  them  were  formed  at 
the  right  hand  side  of  the  wheel  (standing  at  the  point  marked  "A,"  Fig.  408) 
and  towards  the  upper  face  of  the  penstock.  The  water  enters  the  penstock 


A 

Fig.  408. 


from  the  left  hand  side,  flows  through  the  wheel  and  draft  tube  and  off  at 
the  right  hand  side.  The  most  reasonable  explanation  of  this  tendency  for 
the  vortices  to  form  at  the  place  mentioned  was  that  the  wheel,  being  right 
hand,  the  gates  at  the  right  hand  side  of  the  wheel  pointed  upward  (see  Fig- 
ure 410)  and  formed  a  comparatively  direct  path  for  the  vortex  into  the 
wheel,  while  the  gates  on  the  right  hand  side  pointing  downward,  formed  an 
effectual  barrier.  An  examination  of  Figure  409  shows  that  the  left  hand 
edge  of  the  large  raft  does  not  project  beyond  the  gates  so  that  there  was  every 
chance  for  the  vortices  to  form  at  this  point,  yet  none  formed  on  this  side  in 
any  of  the  experiments. 

As  a  result  of  these  preliminary  trials  it  was  decided  to  increase  the  um- 
brella to  10^'  in  diameter,  and  meanwhile  a  test  was  run  off  at  full  gate 
and  three-quarter  gate  opening,  with  the  large  raft  in  place,  to  determine  the 
efficiency  of  the  wheel  under  this  condition.  These  efficiencies  are  shown  on 
the  report  of  the  Holyoke  Water  Power  Company  and  are  numbered  1  to  18. 

It  may  be  here  noted  that  the  Holyoke  Water  Power  Company  finds  it 
necessary  to  use  a  raft  on  practically  all  of  the  horizontal  tests  made  by 


728 


Effect  of  "Umbrella"  Upon  Vortices. 


them,  the  exceptions  being  only  in  the  case  of  the  smallest  wheels,  and  it  is 
the  opinion  of  the  Hydraulic  Engineer  of  that  Company,  as  a  result  of  his 
observations  on  the  various  tests,  that  the  employment  of  rafts  to  prevent  the 
formation  of  vortices  does  not  affect  the  efficiency  of  the  wheels.  This  is 
verified  in  at  least  one  instance,  in  the  test  made  of  two  33"  runners  built 
for  the  <rSoo,"  the  maximum  efficiency  obtained  was  84%,  it  being  necessary 
in  making  this  test  to  use  a  raft,  and  this  efficiency  has  not  been  exceeded 
by  the  same  wheels  when  tested  in  a  vertical  setting  when  no  raft  was  used. 
The  next  test  was  made  on  the  wheel  with  the  enlarged  umbrella  in  place, 
the  edge  of  the  umbrella  being  2'  2"  above  the  center  of  the  shaft,  the  center 
of  the  umbrella  being  in  the  vertical  plane  of  the  shaft.  The  head  of  the 
water  was  16.2'.  With  the  wheel  standing  still  (with  gate  wide  open),  vor- 
tices formed  occasionally,  but  only  for  an  instant,  immediately  disappearing. 
With  the  wheel  allowed  to  run  under  the  brake,  no  vortices  formed,  but  the 


Fig.  410. 

surface  of  the  water  was  disturbed  by  the  formation  of  whirls,  which,  how- 
ever, disappeared  without  becoming  vortices.  This  action  took  place  at  all 
speeds  of  full  gate  opening.  The  same  peculiarities  of  the  action  of  the 
water  were  noticed  under  three-quarter  gate  opening,  but  at  no  time  were 
any  actual  vortices  formed. 

A  test  was  then  made  of  the  wheel  with  the  umbrella  in  the  last  named 
position,  and  the  results  of  this  test  are  noted  under  Nos.  19  to  33  in  the  re- 
port of  the  Holyoke  Water  Power  Company. 

It  was  then  decided  to  suspend  the  umbrella  towards  the  right  side  of  the 
wheel.  With  the  umbella  in  this  position  there  were  no  whirls  or  vortices 
at  any  gate  opening,  and  the  level  of  the  water  was  entirely  smooth  ex- 
cept such  disturbances  as  were  created  by  the  current  of  the  water  flowing 
in.  With  the  umbrella  in  this  position  it  was  decided  to  make  a  few  tests 
to  determine  whether  or  not  there  was  any  difference  in  the  efficiencies  be- 
tween the  two  positions  of  the  umbrella. 

A  test  was  then  made  with  the  head  lowered  about  2'  and  it  was  decided 
to  confine  the  test  to  only  full  gate.  The  action  of  the  water  during  this  test 


Comparison  of  Results.  729 

showed  the  formation  of  irregular  whirls,  but  no  actual  vortices  resulted. 
The  results  of  this  test  are  numbered  38  to  43. 

The  head  was  then  lowered  about  1'.  Under  this  condition  the  level  of  the 
water  was  about  15"  above  the  umbrella.  No  whirls  or  vortices  were  formed 
and  there  was  less  disturbance  to  the  water  than  in  previous  tests,  but  owing 
to  the  method  used  for  changing  the  level  of  the  water  in  the  penstock,  it 
was  necessary  with  the  water  at  this  head,  to  allow  the  incoming  water  to 
fall  over  the  gate  so  that  the  water  when  flowing  into  the  wheel  was  rather 
full  of  air 'bubbles.  The  results  of  this  test  are  numbered  44  to  49. 

The  level  of  the  water  was  then  reduced  2'  more  so  that  the  top  of  the 
umbrella  projected  II"  above  the  level  of  the  water.  Under  this  condition 
there  were  absolutely  no  disturbances  of  the  water,  except  that  it  was  full  of 
air  bubbles  in  the  head  race,  and  upon  examining  the  water  in  the  tail  race  it 
was  found  that  the  water  there  was  also  full  of  air  bubbles.  This  condition 
of  the  water  probably  accounts  for  the  lower  efficiencies  obtained  under  these 
conditions.  The  results  of  the  tests  are  given  in  numbers  50  to  58. 

A  final  test  was  made  with  the  umbrella  raised  so  that  the  top  was  about 
flush  with  the  level  of  the  water.  Under  these  conditions  there  were  small 
whirls  forming  around  the  edge  of  the  umbrella,  but  no  vortices  occurred. 
The  surface  of  the  water  on  the  whole  was  quieter  than  with  the  umbrella 
placed  immediately  above  the  wheel.  The  results  of  this  test  are  numbered 
57  to  65. 

COMPARISON  OF  RESULTS. 

It  must  be  noted  from  an  examination  of  all  of  the  tests  that  the  best  effi- 
ciency obtained  on  this  wheel  was  practically  at  about  .8  gate,  so  that  in 
making  comparisons  for  similar  speeds  under  different  gate  openings,  this 
must  be  allowed  for. 

ONE — Comparing  the  results  obtained  with  the  raft,  numbered  1  to  18, 
with  the  results  obtained  with  the  umbrella  placed  immediately  above  the 
wheels,  numbered  18  to  33:  — 

Take  No.    5  Head  16.09    Revolutions  163         Efficiency  76.18 

No.  24  Head  16.16     Revolutions  161.25    Efficiency  76.51 

Also  No.  25  Head  16.19     Revolutions  164.20     Efficiency  76.05 

These  show  that  the  umbrella,  if  anything,  is  better. 

Take  No.  16  Head  16.95     Revolutions  142.25     Efficiency  78.99 

No.  17  Head  16.93    Revolutions  137.5      Efficiency  79.11 

and  compare  with 

No.  33  Head  16.84    Revolutions  140.5       Efficiency  79.07 
This  also  indicates  that  the  umbrella  is  a  little  better  than  the  raft. 

TWO — Comparing  the  umbrella  at  the  surface  with  the  umbrella  immedi- 
ately above  the  wheel:  — 

Take  No.  61  Head  16.48     Revolutions  158.25     Efficiency  78.7 
No.  25  Head  16.16    Revolutions  157.        Efficiency  76.19 
No.  29  Head  16.8      Revolutions  159.75     Efficiency  74.08, 

show  that  the  umbrella  should  be  placed  near  the  surface  of  the  water. 
Also— 


730  Effect  of  "Umbrella"  Upon   Vortices. 

Take  No.  58  Head  16.53     Revolutions  168.         Efficiency  75.73 
No.  22  Head  16.24     Revolutions  168.75     Efficiency  74.81 
which  indicates  the  same. 

THREE — Comparing  the  results  obtained  in  tests  numbered  38  to  43  with 
those  obtained  in  tests  1  to  18:  — 

Take  No.  43  Head  14.58     Revolutions  129.75    Efficiency  77.36  with 

No.  17  Head  16.93    Revolutions  137.50     Efficiency  79.11 
(Giving  137^  revolutions  at  16.95  head.) 

This  shows  a  falling  off  in  the  efficiency,  but  as  specified  above,  the  point 
of  gate  opening  for  No.  17   is  at  the  point  of  maximum  efficiency  of  the 
wheel,   whereas   the   point   of   gate   opening   under   No.    43    is    considerably 
larger  and  therefore  of  itself  would  be  less  efficient. 
Compare  No.  40  Head  14.62    Revolutions  148.5      Efficiency  77.14 
(Giving  156  revolutions  at  16.07  head)  with 
No.    6  Head  16.07     Revolutions  154.5      Efficiency  75.98 
No.    8  Head  16.08     Revolutions  157.6      Efficiency  76.03 
Also  No.  40  (Giving  160  Revolutions  at  16.99  Head)  with 

No.  12  Head  16.99     Revolutions  159.75     Efficiency  75.09 
The  result  of  these  comparisons  would  show  no  loss  in  efficiency. 

FOUR — Comparing  numbers  44  to  49  with  1  to  18  tests:  — 
No.  47  Head  13.54     Revolutions  138.         Efficiency  77.41 
(Giving  151  Revolutions  at  16.08  Head)  with 
No.  7  Head  16.08     Revolutions  150.         Efficiency  75.63 
Also  No.  47  (Giving  155  Revolutions  at  16.99  Head)  with 
No.  13  Head  15.99     Revolutions  155.5       Efficiency  75.09 

This  shows  no  loss. 

FIVE— Comparing  tests  Nos.  50  to  56  with  1  to  18:  — 
Take  No.  54  Head  11.5      Revolutions  136.        Efficiency  74.92 
(Giving  161  Revolutions  at  16.09  Head)  with 
No.    5  Head  16.09     Revolutions  163.        Efficiency  76.18 

This  shows  a  loss,  as  was  to  be  expected  from  the  condition  of  the  water, 
as  stated  above. 

As  a  result  of  our  calculations  from  the  tests  we  should  say  as  follows:  — 

(A)  That  the  use  of  an  umbrella  or  hood  does  not  reduce  the  efficiency  of 
the  wheel. 

(B)  That  the  hood  should  be  kept  as  close  to  the  surface  of  the  water  as 
possible. 

(Signed)     F.  MOELLER. 


APPENDIX— F. 
EVAPORATION  TABLES. 

Depth  of  evaporation,  in  inches,  at  signal  service  stations,  in  thermometer  shelt- 
ers, computed  from  the  means  of  the  tri-daily  determination  of  dew-point  and 
wet-bulb  observations.* 


Stations  and 
Districts. 


New  England: 

Eastport 

Portland 

Manchester 

Northfield 

Boston 

Nantucket 

Wood's  Holl 

Block  Island 

New  Haven 

New  London 

Mid- Atlantic  States: 

Albany  

New  York  City . . . 

Philadelphia 

Atlantic  City 

Baltimore 

Washington  City. 

Lynchburg 

Norfolk 

So.  Atlantic  States: 

Charlotte 

Hatteras 

Raleigh 

Wilmington 

Charleston 

Columbia 

Augusta 

Savannah  

Jacksonville 

Florida  Peninsula: 

Titusville 

Cedar  Keys 

Key  West 


0.9 
1.0 
0.9 
0.8 
1.2 
1.1 
0.5 
1.1 
1.1 
1.5 


0.9 
1.8 
1.6 
1.2 
2.0 
1.8 
2.6 
1.8 


3.5 
3.3 

3.8 


1.4 
1.2 
1.6 


1.0 
1.6 
1.1 
0.8 
1.1 
1.6 
1.3 


1.2 
1.4 
2.1 
1.6 
2.2 
1.7 
2.7 
1.6 


2.6 
1.6 

1.8 

2.2 
2.5 
2.3 
2.6 
2.8 
2.6 


2.6 
2.8 
3.7 


1.5 
1.8 
2.2 
1.5 


1.2 
1.8 
1.5 


1.6 
2  0 
2.5 
1.5 
2.8 
2  5 
3.4 
2.3 


4.3 
1.6 
2.6 
2 

3 

•> 

3.4 

4.1 
3.8 


/ 
5 

2.6 


4.0 


2.4 
2.6 
3  3 
2.3 
3.4 
1.5 
2.4 
2.0 
2.7 
2.6 


3.3 
3.4 
4.4 
2.4 
5.1 
4.2 
5.2 
3.5 


6.4 
2.5 

3.8 
3  * 
3 

4.8 
5 

4 
4 


3.8 
46 
4.5 


2.5 
1.8 
3.8 
25 
3.1 
1.8 
1.8 
1.8 
2.7 
2.8 


4.5 
2.2 
4.1 
3.3 
3.9 
4.3 
4.8 
4.3 
4.6 


3.8 
4.5 
4.4 


2.7 
3.3 
5.0 
3.4 
4.7 
2.1 
2.7 
2.6 
4.1 
4.0 


4.5 
4.6 
5.7 
3.6 
5.( 
6.0 
5.6 
4.2 


5.8 

3.0 

5. 

4.3 

4.4 

5.4 

5.0 

4.6 

5.3 


4.3 
5.1 

4.8 


=^28   kSS 

3  QC      fl)  GO 

<l^  !CO'- 


2  2 
3.8 
4.1 
3.5 
4.4 
3.3 
2.7 
2.5 
3.7 
3.4 


5.0 
5.0 
5.7 
2.9 
6.0 
5.4 
4.7 
4.6 


4 

4.3 

4.5 

4.2 

4.8 

4.2 

5.0 


3.8 
5.0 
5.1 


2.9 
3.9 
3.3 

9    7 


4.0 
3.8 
2.4 


3.9 


4.7 
5.2 
5.2 


4.0 
4.1 
3.2 
3.1 
4.8 
3.8 
4.5 
4.7 
4.7 


4  3 
5.5 
5.1 


2.5 
3.4 
2.5 
2.3 
3.5 
3.4 
2.7 
2.8 
3.1 
3.2 


3.2 
4.3 
4.3 
2.4 
4.4 
4.1 
3.3 
3.7 


4.6 
3.8 
3.0 
3.9 
4.2 
4.2 
5.1 
3.4 
3.8 


4.0 
4.5 
4. 


31 


2.6 
3.0 
2.8 
1.8 
2.7 
2.7 
1.2 
2.6 
3.2 
3.1 


3.0 
4.1 
4.0 
18 
4.3 
4.2 
3.4 
2.9 


4.0 
3.2 
2.7 
3.4 
4.0 
3.4 
4.1 
3.6 
3.6 


4.1 
4.1 
4.3 


2.2 
2.5 
2.4 
1.1 
2.2 
1.8 
0.8 
1.8 
2.4 
2.4 


2.1 
3.3 
3-3 


4.5 
3.2 
2.3 


?.  6 
2.6 
2.4 
2.8 
3.2 
3.6 
3.6 
3.5 
3.0 


3.6 
3.5 

3.8 


1 
1 
1 
1 
-[ 

1.825.6- 

0. 

1 

1.631.8- 

o 


29.7 
.433.3 
.023.9 

34.4 


.5 


2.1 


434. 


1  . 

2. 

2. 

1.5 

2 

2. 

2.645 

1. 


2.7 


2.1 


3.1 


20.3 
24.0 


31.8 


.8 
.6. 
5.0 
25.2; 
2.448.1 
.6 
.5 
.1; 


240. 
245. 


545, 


S  35 . 


2.649.0- 
1.631  3 
1.837.0 


38.4 


2.543.7 
2.4 
3.1  49.3 
2.846.0 


45.7 


44.2 


2  649.5 
3-6516. 


*From  Monthly  AVeather  Review,  September,  1888. 


732 


Evaporation  Tables. 


Depth  of  evaporation,  In  inches,  at  signal  service  stations— Continued. 


Stations  and 
Districts. 


Eastern  Gulf  States: 

Atlantic 

Pensacola 

Mobile 

Montgomery .... 

Vicksburg 

New  Orleans  .... 

West.  Gulf  States: 

Shreveport 

Fort  Smith 

Little  Rock 

Corpus  Christie  . 
Galveston 

West.    Gulf  State*— 
Continued. 

Palestine 

San  Antonio  . . . 

Rio  Grande  Valley: 
Rio  Grande  City . . 
Brownsville 

Ohio  Valley  and 
Tennessee: 

'Chattanooga 

Knoxville 

Memphis 

Nashville 

Louisville 

Indianapolis 

Cincinnati 

Columbus 

Pittsburg 

Lower  Lake  Region. 

Buffalo 

Oswego 

Rochester 

Erie 

Cleveland 

Sandusky  

Toledo 

Detroit 

Upper  Lake  Region, 

Alpena  

Grand  Haven 

Lansing 

Marquette 

Port  Huron 

Chicago 

Milwaukee 

Green  Bay 

Duluth 


2.9 
2.6 
3 
2.1 

2.8 


1.6 
2.2 
2.1 
1.4 
1.6 


2.1 
2.4 


2.7 

1.8 


2.0 
2.4 
2.1 
1.9 


1.4 


0.8 
0.6 


1.1 


o 
0 
0.8 


o 

1 

0 
0 
0.5 


2.6 
2.8 
2.5 
3.3 
2.5 
2.8 


2.1 
2.7 
2.8 
1.6 

2.8 


3.0 
3.3 


3.5 
2.6 


3.3 
2.6 
2.3 
2.1 
2.1 
1.4 
1.8 
2.0 


1.1 
1.0 
1.1 
1.4 
1.4 
1.4 
1.1 
1.1 


0.6 

0. 

1.2 

0.8 

1.0 

1.2 

1.0 

0.6 

0.5 


4.0 
4.1 
2.8 
5.1 
3.6 
4.1 


3.0 
3.5 
3.5 
3.3 
3.2 


3.3 
4.1 


3.5 
2.9 


3.3 
3.4 
3.1 
3.2 
2.8 
2.2 
2.6 
2.3 
2.2 


1.3 
1.1 
0.9 
1.4 
1.5 
1.5 
1.5 
1.6 


0.9 
.3 
,4 
,9 

.1 

.8 
.1 

0.8 
0.6 


6.2 
4.0 
3.5 
6.5 
5.1 
3  8 


4.8 
5.3 
5.5 
3.0 
2.9 


4.2 

3.8 


3.6 
3.0 


5.3 
5.0 
5.9 
5.9 
5.6 


2.2 
2.2 
2.6 
2.7 
2.9 
3.2 
3.5 
3.0 


1.6 
2.6 
2.7 
1.7 
2.6 
3.2 
2-4 
1.7 
1.5 


4.7 
4.3 
3.7 
5.9 

5.7 
4.2 


4.9 
4.4 
4.8 
3.2 
4.3 


4.3 
4.0 


4.5 
3.5 


3.7 
3.5 
5.3 
5.0 
5.4 
4.8 
5.2 
4.8 
4.2 


3.3 
2.8 
3.8 
3.7 
3.3 
3.7 
3.8 
4.1 


2.1 
3.1 
2.8 
2.4 
3.0 
3.3 
2.6 
2.5 
2.4 


5 

4 

4 

5.8 

4.8 

4.1 


4.2 
4.H 
4.1 
3.9 
4.2 


4.5 
4.5 


4.6 
3.9 


4.3 
4 

4.8 

5.1 

5.8 

5 

6.4 

5.8 

5.4 


3.9 

3.8 


4 
4 
4.4 


4.6 

4.8 


3.6 
3.8 
4.0 
3.3 
3.8 
4.8 
3.8 
4.1 
2.5 


>>!>- 

co 

3  CO      ~  GO 


4.5 
5.0 
4.1 


4-1 


4.9 
5.6 
5  4 
4.4 
5.3 


5.8 
6.6 


6.9 
4.0 


4.3 
4.9 
4.9 
5.5 

6.8 
7.7 
6.5 
6.9 
6.6 


4.9 


5.5 
5.2 
5.4 
6.0 
5.9 


3.4 
4.6 
5.4 
4.8 
5.6 
3.9 


4.7 
5.4 
4.6 
4.5 
5.0 
4.3 


5.2 
4  6 
5.9 
4.3 
5.2 


4.6 

5.8 


7.0 
4.1 


5.o 
5.0 
5.4 
6.3 
7.4 
6.9 
6.6 
6.4 
5.6 


5.2 


5.2 


3.7 
3.8 
3.9 
3.3 
4.2 
5.3 
3.7 
4.2 
3.4 


5.8 
5.2 
4.6 
5.7 
4.7 
4.4 


5.0 

4.7 

5. 

4.3 

5.2 


4.8 
5.2 


5.2 
3.3 


5.4 
4.9 
5.5 
5.9 
6.4 
5.2 
6.1 
5.1 
4.9 


3.9 
3.6 
3.8 
3.1 
3.8 
3.7 
3.7 
3.4 


2.8 
2.7 
2.4 
3.1 
3.2 
4.1 
3.4 
3.0 
3.0 


4.6 
4.5 
4  1 
4.6 
3.4 
4.6 


4.1 
5.9 
5.2 
4.1 
4.7 


4.4 
5.4 


4.9 
3.0 


4.2 
4.0 
4.9 
4.1 
4.7 
4.0 
3.4 


2.8 
2.7 
2.6 
2.5 
3.4 
3.4 
3.4 
2.8 


2.2 
2.6 
1.9 
2.2 
2.5 
3.2 
2.9 
2.4 
2.5 


Hi! 


4.2 
3.6 
3.4 
4.3 
4.0 
3.7 


3.4 
3.9 
4.3 
3.0 
4.2 


4.0 
4.2 


3.6 

2.6 


3.9 
3.8 
4.1 


3.1 
3.3 

2.6 

2.8 


1.9 
2.2 
2.2 
1.9 
2.4 
2.2 
2.4 
2.0 


1.5 
1.7 
1.4 
1.3 
1.7 
2.3 
1.9 
1.9 
1.2 


2.5 
2.4 
2.2 
3.1 
2.2 


9  s 


oi.o 
48.8 
42.1 
56.6 
1 
45.4 


247 


2.445.6 
2.249.6 
2.35L.7 
2.338.8 
2.4146.0 


2.1 
3.1 


3.1 


47.1 
52.4 


53.1 


1.946.4 


2.1 


45.9 


2.4 


50.0 
50.1 
1J54.8 


1.648.6 


2.1 


52.0 


1.847.8 
2.344.5 


1.632.9 
T028.9 


435.7 
336.6 
338.6 


1.336.0 


28.6 


027.6 
24,5 

029.3 

236.8 
29.0 

9  28 . 2 


23.0 


Evaporation  Tables. 


733 


Depth  of  evaporation,  in  Inches,  at  signal  service  stations — Continued. 


Stations  and 
Districts. 

o!  GO 

£1 

Si 

il 

30    >>GC 

11 

3§ 

fi 

i| 

si 

§1 

l| 

00 
CO 

! 

"~5              i 

** 

Extreme  Northwest: 
Moorhead  
Saint  Vincent  
Bismarck  
Fort  Buford  
Fort  Totten  

Upper  Mississippi 
Valley: 
St.  Paul  
LaCrosse  
Davenport  
DesMoines  
Dubuque  
Keokuk            .... 

0.2 
0.3 
0.4 

1.4 
0.2 

0.7 
0.4 
0.5 
0.6 
0.7 
0.8 
1.6 
0.8 
1.3 

1.1 

1.1 
0.9 
1.1 
0.8 
0.7 
1.2 
0.6 
0  3 

1.4 
0.3 
0.6 
0.7 
0.3 

0.7 
1.2 
1.0 
1.0 
1.0 
1.1 
2.1 
1.1 

1.6 

1.6 
1.7 
1.5 
1.2 
1.5 
1.1 
1.6 
0.9 
0.7 

0.5 
0.5 
0.6 
0.6 
0.4 

2.2 

1.4 
1.8 
1.5 
1.4 
2.1 
2.9 
2.0 
2.5 

2.4 
2.4 
2. 
2. 
1. 
1. 
1. 
1. 
0 

2.1 

1.8 
3.0 
3.0 

2.2 

2.0 
3.3 
3.8 
3.7 
2.2 
4.2 
5.8 
4.6 
5.5 

4.4 
5.0 
4.6 
4.0 
4.4 
3.5 
5.0 
4.4 
3  7 

3.6 
3.8 
4.3 
4.7 
4.6 

2.3 
3.5 
3.4 
3.1 
2.9 
3.7 
4.4 
3.8 
4.7 

3.8 
4.8 
4.5 
4.1 
3.8 
3.3 
3.2 
4.1 
3  7 

3.8 
3.9 
4.1 
5.0 
3.8 

4.1 
4.4 
4.6 
4.2 
4.2 
4.3 
4.3 
4.3 
5.0 

4.0 
4.0 
5.0 
4.1 
5.2 
4.5 
5.3 
5.2 
4  1 

3.7 
3.1 
5.6 
6.2 
4.2 

5.0 
5.4 
6.9 
6.6 
6.2 
7.0 
5.6 
5.4 
7.5 

6.0 
5.0 
6.3 
6.3 
6.2 
5.6 
6.9 
7.7 
5  7 

3.3 
2.6 
4.2 
4.9 
3.7 

3.7 
4.7 
6.2 

4.7 
4.8 
6.8 
6.5 
6.5 
8.0 

4.6 
3.4 
4.5 
3.5 
5.2 
4.7 
5.0 
4.9 
4  9 

3.5 
2.6 
4.0 

4.8 
3.7 

2.8 
3.0 
4.4 
4.1 
3.3 
5.0 
5.1 
4.5 
5.9 

3.7 
3.4 
4.0 
3.2 
4.3 
3.8 
5.2 
5.7 
4  1 

2.4 
2.0 
2.6 
3-0 
2.3 

2.4 
3.0 
3.0 
3.3 
2.8 
3.8 
4.5 
3.5 
4.9 

3.6 
3.5 
3.9 
3.0 
4.3 
3.6 
3.8 
3.6 
3  1 

1.3 
0.9 

1.2 
1.7 
1.4 

1.5 
1.8 
2.3 
2.3 
1.8 
2.9 
3.8 
2.9 
3.9 

2.9 
3.1 
2.7 
2.2 
3.0 
2.4 
3.3 
2.8 
?,  4 

0.5 
0.3 
0.4 
0.5 
0.4 

0.7 
0.8 
1.1 
0.9 
0.9 
1.2 
2.3 
1.4 
1.4 

1.5 
1.4 
A 
.4 
.4 
.1 
.5 
0.7 
0  7 

26.3 
22.1 
31.0 
35.5 

27.2 

28.1 
32.9 
39.0 
36.0 
33.2 
42.9 
48.9 
40.8 
52.2 

39.6 
38.3 
41.6 
36.1 
41.7 
35.5 
43.8 
41.9 
33  0 

Cairo         .  .       ... 

Springfield,  111.  .  .  . 
St.  Louis  

Missouri  Valley: 
Lamar           

Springfield,  Mo.  .  . 
Leaven  worth  
Topeka  
Omaha  

Crete  

Valentine  

Fort  Sully  
Huron 

Yankton 

0.4 

0.8 
0.6 
1.1 

1.4 

1.2 
1.5 
1.4 
3  6 

1. 

1. 
1. 
1.1 

2  1 

3.3 

3.8 
5.4 
3.3 
6  1 

3.1 

4.1 
6.8 
3.2 
4  3 

4.4 

4.2 

4.9 
4.6 
5  5 

4.6 

6.8 
9.6 
6.8 
7.2 
6.0 
8.0 
6.0 

6.7 
8.3 
3.0 
7.3 
8.3 
7.6 

4.8 
9.5 
11.4 
9.4 

3.7 

5.5 

8.0 
4.6 

7.7 
4.8 
7.7 
4.8 

7.2 
8.5 
4.0 
5.2 
6.6 
6.2 

7.5 

7.5 
9.0 
11.6 

2.9 

4.8 
6.1 
3.8 
6.4 
4.4 
8.6 
3.7 

6.8 
6.1 
3.0 
4.3 
5.5 
5.4 

5.1 
6.2 
5.9 
3.9 

3.0 

3.5 
3.4 

2.8 
4.3 
2.5 

5.8 
2.8 

4.6 
4.9 
2.3 
4.5 
5.2 
4.7 

4.2 
4.5 
5.2 
4.0 

2.2 

2.5 
2.9 
2.0 
3.0 
1.7 
6.1 
2.3 

4.2 
4.2 

2.8 
3.4 
4.2 
4.2 

4.1 
3.4 
5.7 
3.6 

0.8 

1.1 
1.5 
1.1 
2.1 
0.7 
3.5 
1.1 

2.9 
3.1 
1.0 
1.8 
2.1 
2.2 

2.0 
1.7 
4.9 

3.8 

31.0 

39.5 
52.0 
35.8 
53.4 
35.4 
76.5 
41.3 

59.4 
69.0 
26.8 
47.2 
54.6 
55.4 

46.1 
54.4 
96.4 
76.0 

Northern  Slope: 
Fort  Assimboine.. 
Fort  Custer 

Fort  Maginnis  .... 

Poplar  River 

0.4 
3.3 

0.8 

3-0 
2.8 
2.1 
1.3 
1.4 
1.3 

1.6 
1.8 
5.4 
3.9 

0.8 
5.7 

1.8 

3.3 
3.7 
1.3 
2.8 
2.4 
1.9 

2.0 
1.7 
5.7 
3.9 

0.8 
4.0 
1.8 

4.1 
3.5 
1.5 

1.8 
2.8 
3.2 

3!l 
6.7 
5.2 

2.7 

8.2 
5.4 

6.7 
7.6 
2.1 
4.8 
4.1 
5.1 

3.8 
4.2 
8.5 
7.3 

4.9 
5.2 
3.9 

5.6 
5.8 
1.8 
4.3 
4.6 
5.4 

4.0 
5.0 
11.0 
9.5 

5.7 

10.4 
6.9 

4.3 

10.5 
1.9 
5.7 
7.4 

8.2 

4.4 

5.8 
12.0 
10.9 

Cheyenne  
North  Platte 

Middle  Slope: 
Colorado  Springs. 
Denver  
Pike's  Peak 

Concordia     

Dodge  City  
Fort  Elliott  

Southern  Slope; 
Fort  Sill 

Abilene  
Fort  Davis  
Fort  Stanton  

734 


Evaporation  Tables. 


Depth  of  evaporation,  in  inches,  at  signal  service  stations—  Continued. 


Stations  and 
Districts. 

if 

m 

*i 

_ 

11 

B  co 

I*! 

?i 

II 

|i 

si 

11 

I 

r* 

Southern  Plateau: 

El  Paso  

4.0 

3.9 

6.0 

8.4 

10.7 

13.6 

9.4 

7.7 

5.6 

5.2 

4.6 

2.9 

82.0 

Santa  Fe 

3.0 

3.4 

4.2 

6.8 

8.8 

12.9 

9.2 

9.8 

6.6 

6.7 

5.7 

2.7 

79.8 

Fort  Apache  .... 

2.6 

3.0 

3.6 

6.8 

9.4 

9.1 

7.1 

6.7 

5.3 

5.2 

4.1 

2.6 

65.5 

Fort  Grant  

5.2 

4.8 

6.4 

9.2 

10.2 

13.8 

12.4 

10.5 

9.0 

7.9 

7.2 

4.6 

101.2 

Prescott  

1.4 

2.8 

3.6 

5.4 

6.2 

8.1 

6,6 

6.5 

4.7 

4.9 

3.6 

2.2 

56.0 

Yuma  

4.4 

5.2 

6.6 

9.6 

9.6 

12.6 

11.0 

10.2 

8.2 

8.2 

5.5 

4.6* 

95.7 

Keeler  

3.0 

4.6 

6.3 

8.7 

9.3 

11.9 

12.8 

13.9 

10.6 

8.8 

5.9 

4.8 

100.6 

Middle  Plateau: 

Fort  Bidwell  .... 

0.8 

1.8 

1.8 

4.6 

5.2 

4.0 

8.8 

8.1 

5.0 

4.6 

2.4 

1.3 

48.9 

Winnemucca  .... 

0.9 

2.8 

6.2 

9.1 

9.3 

10.1 

11.5 

12.0 

9.9 

6.6 

3.7 

1.8 

83.9 

Salt  Lake  City.  .  . 

1.8 

2.7 

3.6 

7.2 

6.9 

8.9 

9.2 

10.7 

9.6 

6.5 

5.0 

2.3 

7.44 

Montrose  

1.8 

2.7 

3.7 

6.2 

7.0 

11.1 

10.2 

8.3 

6.9 

5.2 

3.4 

2.0 

68.3 

Fort  Bridger  

1.6 

2.5 

2.7 

4.3 

4.3 

6.5 

7.7 

6.8 

5.6 

4-2 

5.2 

4.7 

56.1 

Northern  Pleat  eau: 

Boise  City  

1.6 

2.5 

3.8 

6.1 

6.5 

6.6 

10.0 

9.2 

7.4 

5.2 

3.2 

1.8 

63.9 

Spokane  Falls.  .  . 

0.7 

1.7 

2.7 

4.4 

5.4 

4.4 

7.7 

6.4 

3.8 

2.5 

1.7 

1.4 

42.8 

Walla  Walla.... 

1.1 

2.9 

3.6 

6.2 

7.7 

5.7 

9.9 

7.9 

5.1 

3.4 

1.8 

2.4 

57.7 

No.  Pacific  Coast:. 

Fort  Canby  

1.2 

1.1 

1.8 

2.1 

2.8 

2.3 

1.8 

2.9 

1.8 

1.8 

1.5 

0.9 

21.1 

Olynipia  

1.3 

1.2 

1.8 

2.5 

4.1 

3.3 

3.2 

3.1 

2.4 

1.5 

1.3 

1.1 

26.8 

Port  Angeles  .... 

1.0 

0.9 

1.8 

1.8 

2.5 

2.1 

2.1 

1.8 

1.5 

1.2 

1.3 

1.1 

19.1 

Tatoosh  Island.  . 

1.2 

1.1 

1.8 

1.4 

1.8 

1.8 

1.4 

1.4 

1.4 

1.6 

1.8 

1.4 

18.1 

Astoria 

1.1 

1.0 

1.6 

2.1 

3.0 

2.7 

3.0 

2.9 

2.6 

2.3 

1.8 

1.2 

25.3 

Portland 

0.9 

1.1 

2.4 

3.4 

5.0 

3.2 

5.4 

4.2 

3.4 

2.7 

1.8 

1.2 

34.7 

Roseburg  

1.2 

1.6 

2.7 

3.9 

4.7 

3.5 

5.4 

4.7 

5.0 

3.2 

1.7 

1.6 

39.2 

Middle  Pacific 

Coast: 

"Red  Bluff  

3.0 

4.6 

5.4 

6.1 

7.0 

6.9 

11.0 

10.7 

10.1 

10.5 

5.9 

3.6 

84.8 

Sacramento  

1.8 

3.1 

3.7 

4.3 

4.2 

5.6 

5.9 

5.6 

6.5 

7.3 

3.9 

2.4 

54.3 

San  Francisco.  .  . 

2.7 

2.7 

3.3 

3.1 

2.8 

3.1 

2.4 

2.5 

3.3 

5.0 

2.8 

3.0 

36.7 

So.  Pacific  Coast: 

Fresno  

1.8 

2.8 

3.0 

5.6 

6.0 

7.0 

9.1 

10.2 

7.6 

6.7 

3.8 

2.2 

65.8 

Los  Angeles  

2.3 

2.0 

2.8 

3.4 

3.0 

3.8 

3.2 

3.5 

3.1 

4.1 

3.0 

3.0 

37.2 

San  Diego  

2.9 

2.7 

2.5 

2.7 

3.3 

2.8 

3.2 

3.3 

2.9 

4.3 

3.2 

3.7 

37.5 

APPENDIX.— G. 

TWO  NEW  WATER  WHEEL   GOVERNORS. 

The  Glocker- White  Turbine  Governor.— The  I.  P.  Morris  Com- 
pany has  built  a  governor  for  the  Electrical  Development  Company 
of  Ontario.,  Canada,  which  has  one  novel  feature-*  A  cross  section 
of  its  distinctive  feature  is  shown  in  Fig.  411. 

The  governor  ball  is  hollow  and  contains  two  chambers,  a  and  b, 
communicating  with  each  other  through  a  small  opening,  c. 

The  balls  are  partially  filled  with  mercury  which,  when  running 
at  normal  speed,  the  axis  of  the  ball  being  vertical,  is  divided  be- 
tween the  two  chambers.  When  an  increase  of  speed  throws  the 
balls  outward,  centrifugal  force  causes  a  flow  of  mercury  from 
chamber,  a,  to  chamber,  b.  This  raises  the  center  of  gravity  of  the 
ball  and  increases  its  lever-arm  about  the  knife  edge,  j,  thus  increas- 
ing its  effectiveness  by  making  its  movement  increase  in  a  greater 
ratio  than  the  speed  increases.  Similarly  a  reduction  in  speed  causes 
the  balls  to  incline  inward  and  the  mercury  therefore  to  flow  from 
chamber,  b,  to  chamber,  a,  which  tends  to  cause  a  still  greater  in- 
ward inclination. 

The  charge  of  mercury  hence  increases  the  sensitiveness  of  the 
governor  balls  to  small  changes  in  speed. 

The  centrifugal  force  of  the  balls  is  resisted  through  knife  edges, 
K,  K,  by  a  spiral  spring.  This  movement  is  transmitted  by  levers 
to  a  small  pilot  valve  which  controls  a  larger  relay  valve  admitting 
oil  under  250  pounds  pressure  to  the  cylinder.  The  gate  to  be  moved 
is  a  cylinder  gate  opening  upward,  a  force  of  15,000  pounds  being 
required  for  the  purpose.  The  weight  of  the  gate  is  sufficient  to 
close  it  and  the  power-cylinder  of  the  governor  is  therefore  made 
single  acting.  The  entire  governor  is  not  shown  as  there  are  no 
other  unusual  features. 

The  Allis-Chaimers  Governor.— This  Company  has  recently  de- 
veloped a  water  wheel  governor,  the  following  description  of  which 
is  taken  from  their  bulletin  No.  1612: 


*  See  "The  Glocker-White  Turbine  Governor"  by  W.  M.  White  and  L.  F. 
Moody  in  "Power,"  Aug.  4,  1908. 


736 


Two   New  Water  Wheel  Governors. 


Fig.  411.— Cross-Section  of  the  Glocker-White  Governor  Head. 


The  Allis-Chalmers  Governors. 


737 


''The  Allis-Chalmers  Governor  is  of  the  oil  pressure  type  and  con- 
sists of  three  distinct  elements : 

"First — Governor  Stand  (see  Fig.  4i2)  containing  the  apparatus 


10 


DISCHARGE 


Fig.  412. — View  of  the  Governor  Stand  of  the  Allis  Chalmer  Governor. 

for  controlling  the  time  of  application  of  energy  for  actuating  the 
gates- 

"Second — Regulating  Cylinder  for  applying  energy. 

"Third — Pressure  System  for  supplying  energy. 
45 


738  Two  New  Water  Wheel  Governor. 

"The  Governor  Head  (i),  designed  to  be  a  highly  sensitive  yet 
stable  apparatus  and  driven  from  the  Turbine  Shaft  by  Pulley  (2), 
forms  the  basic  governing  element.  Any  change  in  its  position 
moves  the  Governor  Collar  (18),  thereby  shifting  the  Floating 
Lever  (3),  and  through  it  and  its  connection  with  the  Relay  (4) 
(which  momentarily  acts  as  a  stationary  fulcrum)  actuates  the  Reg- 
ulating Valve  (9).  Any  movement  of  this  Regulating  Valve  admits 
oil  from  the  Pressure  System  to  either  the  opening  or  closing  side 
of  the  Regulating  Cylinder  and  thereby  actuates  the  Turbine  gates. 
The  Relay  (4)  forms  a  mechanical  connection  between  the  Regu- 
lating Cylinder  Piston  and  the  Floating  Lever  (3),  constituting  what 
may  be  termed  a  moving  fulcrum,  so  that  every  movement  of  the 
Regulating  Piston  shifts  the  fulcrum  point  and  brings  the  Regu- 
lating Valve  (9)  back  to  mid  position,  thereby  making*  the  mechan- 
ism "dead  beat."  If  this  movement  is  adjusted  so  that  the  position 
of  these  parts  have  the  proper  relation,  the  Governor  Collar  will 
practically  retain  a  fixed  position. 

'The  Regulating  Cylinder  cannot  however,  fully  open  or  close 
the  turbine  gates  instantaneously  and  the  above  result  can  only  be 
obtained  within  certain  limits,  a  difference  of  speed  occurring  be- 
tween no  load  and  full  load  that  requires  a  certain  movement  or 
travel  of  the  Governor  Collar  (18).  Consequently,  the  speed  of  the 
Turbine  at  different  gate  openings  will  vary  slightly  and  depend 
upon  the  speed  of  the  Governor  at  corresponding  positions  of  the 
Regulating  Piston  Stroke. 

"Under  favorable  conditions  (open  flume  and  short  penstocks) 
the  opening  and  closing  time  of  the  gates  depends  solely  upon  the 
inertia  of  the  moving  masses  and  "aperiodical  regulation"  can  be 
obtained;  i.  e.,  the  stroke  of  the  Regulating  Piston  and  the  travel 
of  the  Governor  Collar  correspond  in  time.  Under  favorable  con- 
ditions (long  penstocks)  the  closing  time  is  often  so  influenced  by 
the  "critical  time,"  already  mentioned,  and  by  other  considerations 
that  "aperiodical  regulation"  is  no  longer  practicable  since  a  travel 
of  Governor  Collar  would  be  required  that  would  cause  a  greater 
difference  in  speed  between  no  load  and  full  load  than  is  commer- 
cially allowable.  To  meet  such  conditions,  the  '"Compensating 
Dash  Pot"  (7)  is  utilized. 

"In  the  diagram,  Fig.  413,  the  full  travel  of  the  Governor  Collar 
is  shown  as  corresponding  to  a  speed  change  "x"-  The  Relay 
Stroke,  however,  is  designed  so  that  only  a  portion  of  this  travel 
corresponding  to  a  speed  change  "y"  is  utilized;  i.  e./ within  this 


The  Allis-Chalmers  Governor. 


739 


limit  the  Governor,  without  other  mechanism  than  the  Relay,  is 
''dead  beat"  and  the  Regulating  Valve  by  relay  action  is  returned 
to  mid-position  after  each  movement.  The  Compensating  Dash 
Pot,  (7),  consists  of  a  cylinder  having  an  adjustable  bypass  and 
containing  a  compound  piston,  with  auxiliary  spring  device,  the  rod 
of  which  is  connected  through  a  suitable  lever  to  the  Governor  Col- 
lar. Arranged  so  that  its  piston  takes  motion  from  the  Relay  actu- 
ating shaft,  is  a  positive  displacement  pump  connected  by  a  pipe  to 
the  "Compensating  Dash  Pot"  cylinder.  For  slight  changes  of 


Fig.  413. — Diagram  of  Allis-Chalmers  Governor. 

load,  a  negligible  displacement  of  oil  takes  place  and  the  Dash  Pot 
has  a  slight  damping  action  only  on  the  governor  head,  but  when 
any  load  change  occurs  of  sufficient  magnitude  to  produce  a  speed 
variation  greater  than  "y"  as  shown  on  the  diagram,  enough  oil  dis- 
placement takes  place  to  bring  the  auxiliary  spring  effect  of  the 
Dash  Pot  piston  strongly  into  action  until  the  fluctuation  is  con- 
trolled and  the  Governor  Collar  is  again  brought  within  the  limits 
corresponding  to  "y"  speed  variation  when  action  ceases.  By  this 
means,  a  governing  element  of  maximum  sensitiveness  can  be  used 
and  the  regulation  of  ordinary  slight  fluctuations  made  "aperiodical", 
even  under  the  most  unfavorable  conditions.  These  elements  in 
design,  therefore,  result  in  the  Allis-Chalmers  Governor  operating 
with  great  quickness  and  holding  the  speed  variation,  due  to  ordi- 
nary fluctuations,  within  the  narrowest  limits,  yet  being  absolutely 
safe  from  hunting  or  overtravel  after  heavy  load  fluctuation,  even 
under  the  most  difficult  operating  conditions." 


APPENDIX— H. 

MISCELLANEOUS  TABLES. 

TABLE  LXXVIIL 


EQUIVALENT  MEASURES  AND  WEIGHTS  OF  WATER 
AT  4°  CENTIGRADE—  39.2°  FAHRENHEIT. 

u.  s. 

Gallons 

Imperial 
Gallons 

Liters 

Cubic 
Meters 

Pounds 

Cubic 
Feet 

Cubic 
Inches 

Circular 
Inch 
1  Foot 
Long- 

1 

.83321 

3.7853 

.0037853 

8.34112 

.13368 

231 

24.5096 

1.20017 

1 

4.54303 

.004543 

10.0108 

.160439 

277.274 

29.4116 

.264179 

.22012 

1 

.001 

2.20355 

.035316 

61.0254 

6.4754 

264.179 

220.117 

1000 

1 

2203.55 

35.31563 

61025.4 

6475.44 

.119888 

.099892 

.453813 

.0004538 

1 

.0160266 

27.694 

2.9411 

7.48055 

6.23287 

28.3161 

.0283101 

62.3961 

1 

1728 

183.346 

.0043^9 

.003607 

.0163866 

.0000164 

.0361089 

.0005787 

1 

.10613 

.0408 

.034 

.1544306 

.0001544 

.340008         .005454 

9.4224 

1 

TABLE  LXXIX. 


EQUIVALENT  UNITS  OF  ENERGY 

WORK 

HEAT 

ELEC- 
TRIC 

HYDRAULICS 

'S 

II 

Foot  Ton 
2240  Lbs. 

Kilogram 
Meter 

is 

§® 
EHS 

*£ 

65  il 

«e£ 

"c  S 
®  wg 
'E^  bt 

Sti.2 

oc3 

Volt 
Columb 

d 

^3 

8* 

feO 

si 
S.8 

11 
11 

PL|O 

^rtf 
10 

PnU 

1 

.000446 

1383 

.000138 

.001285 

.000324 

.000377 

.12 

.016 

.0519 

.0069 

2240. 

1 

309.688 

.3097 

2.8785 

.7262 

.8439 

268.817 

35.906 

116.414 

15.456 

7.233 

.00323 

1 

.001 

.0093 

.00235 

.00272 

.8673 

.1159 

.3755 

.0499 

7233.18 

3.2291 

1000 

1 

9.302 

2.3452 

2.7241 

867.303 

115.928 

375.516 

49.90 

778. 

.3474 

107.562 

.1076 

1 

.2520 

.2929 

93.28 

12.448 

40.394 

5.368 

3085.34 

1.3774 

426-394 

.4264 

3.9683 

1 

1.1623 

370.17 

49.396 

160.29 

21  .  221 

2655.4 

1.1854 

371.123 

.3671 

3.414 

.8603 

1 

318.39 

42-486 

137.87 

183.23 

8.341 

.00372 

1.1532 

.00115 

.1072 

.0027 

.00314 

1 

.1334 

.4as 

.05754 

62.39 

.02785 

8.6257 

.00863 

.0803 

.00202 

.02353 

7.48 

1 

3.245 

.4312 

19.259 

.00859 

2.6626 

.00266 

.0248 

.00624 

.00726 

2.309 

.3082 

1 

.13-9 

144.92 

.0647 

20.036 

.02004 

.1863 

.04712 

.05457 

17.37 

2.318 

7.524 

1 

Theoretical  Jet  Velocities. 


741 


TABLE  LXXX. 

Velocities,  in  feet  per  second,  due  to  Heads— from  0  to  50  feet. 


Head 
in 
feet. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

0  

0.000 

2.536 

3.587 

4.393 

5.072 

5.671 

6.212 

6.710 

7.178 

7.609 

1  

8.020 

8.412 

8.786 

9.144 

9.490 

9.823 

10.145 

10.457 

10.760 

11.055 

2  

11.342 

11.622 

11.896 

12.163 

12.425 

12.681 

12.932 

13.179 

13.420 

13.658 

3  

13.891 

14.121 

14.347 

14.569 

14.789 

15.004 

15.217 

15.427 

15.634 

15.839 

4  

16.040 

16.240 

16.437 

16.631 

16.823 

17.013 

17.201 

17.387 

17.571 

17.753 

5  

17.934 

18.112 

18.289 

18.464 

18.637 

18.809 

18.979 

19.148 

19.315 

19.481 

6  

19.645 

19.808 

19.970 

20.131 

20.290 

20.448 

20.604 

20.760 

20.914 

21.067 

7  

21.219 

21.370 

21.520 

21.669 

21.817 

21.964 

22.110 

22.255 

22.399 

22.542 

8.'.'.'.'. 

22.685 

22.826 

22.966 

23.106 

23.245 

23.383 

23.520 

23.656 

23.792 

23.927 

9  

24.061 

24.194 

24.326 

24.458 

24.589 

24.720 

24.850 

24.979 

25.107 

25.235 

10  

25.362 

25.489 

25.614 

25.740 

25.864 

25.988 

26.112 

26.235 

26.357 

26.479 

11  

26.600 

26.721 

26.841 

26.960 

27.079 

27.198 

27.316 

27.433 

27.550 

27.667 

12  

27.783 

27.898 

28.013 

28.128 

28.242 

28.356 

28.469 

28.582 

28.694 

28.806 

18  

28.917 

29.028 

29.139 

29.249 

29.359 

29.468 

29.577 

29.686 

29.794 

29.901 

14  

30.009 

30.116 

30.222 

.30.329 

30.435 

30.540 

30.645 

30.750 

30.854 

30.958 

15  

31.062 

31.165 

31.268 

31.371 

31.474 

31.576 

31.677 

31.779 

31.880 

31.980 

16  

32.081 

32.181 

32.281 

32.380 

32.480 

32.579 

32.677 

32.775 

32.873 

32.971 

17  

33.068 

33.165 

33.262 

83.359 

33.455 

33.551 

33.647 

33.742 

33.837 

33.932 

18  

34.027 

34.121 

34.215 

34.309 

34.403 

34.496 

34.589 

34.682 

34.775 

34.867 

19  

34.959 

35.051 

35.143 

35.234 

35.325 

35.416 

35.507 

35.597 

35.688 

35.778 

20  

35.867 

35.957 

36.046 

36.135 

36.224 

36.313 

36.401 

36.490 

36.578 

36.666 

21  

36.753 

36.841 

36.928 

37.015 

37.102 

37.188 

37.275 

37.361 

37.447 

37.532 

22  

37.618 

37.703 

37.789 

37.874 

37.959 

38.043 

38.128 

38.212 

38.296 

38.380 

23  

38.464 

38.547 

38.630 

38.714 

38.797 

38.879 

38.962 

39.014 

39.127 

39.209 

24  

39.291 

39.373 

39.454 

39.536 

39.617 

39.698 

39.779 

39.860 

39.940 

40.021 

25  

40.101 

40.181 

40.261 

40.341 

40.421 

40.500 

40.579 

40.659 

40.738 

40.816 

26  

40.895 

40.974 

41.052 

41.130 

41.209 

41.287 

41.364 

41  .442 

41.520 

41.597 

27  

41.674 

41.751 

41.828 

41.905 

41.982 

42.058 

42.135 

42.211 

42.287 

42.363 

28  

42.439 

42.515 

42.590 

42.666 

42.741 

42.816 

42.891 

42.966 

43.041 

43.116 

29  

43.190 

43.264 

43.839 

43.413 

43.487 

43.561 

43.635 

43.708 

43.782 

43.855 

30  

43.928 

44.002 

44.075 

44.148 

44.220 

44.293 

44.366 

44.438 

44.510 

44.582 

31  

44.655 

44.727 

44.798 

44.870 

44.942 

45.013 

45.085 

45.156 

45.227 

45.298 

3-2  

45.369 

45.440 

45.511 

4?,.  581 

45.652 

45.722 

45.792 

45.863 

45.933 

46.003 

33  

46.073 

46.142 

46.212 

46.281 

46.351 

46.420 

46.489 

46.559 

46.628 

46.697 

31  

46.765 

46.834 

46.903 

46.971 

47.040 

47.108 

47.176 

47.244 

47.312 

47.380 

85  

47.448 

47.516 

47.584 

47.651 

47.719 

47.786 

47.853 

47.920 

47.987 

48.054 

36  

48.121 

48.188 

48.255 

48.321 

48.388 

48.454 

48.521 

48.487 

48.653 

48.719 

37  

48.785 

48.851 

48.917 

48.982 

49.048 

49.113 

49.179 

49.244 

49.310 

49.375 

38  

49.440 

49.505 

49.570 

49.635 

49.699 

49.764 

49.829 

49.893 

49.958 

50.022 

39  

50.086 

50.150 

50.214 

50.278 

50.342 

5D.406 

50.470 

50.534 

50.597 

50.661 

40  

50.724 

50.788 

50.851 

50.914 

50.977 

51.040 

51.103 

51.166 

51.229 

51.292 

41  

51.354 

51.417 

51.479 

51.542 

51.604 

51.667 

51.729 

51.791 

51.858 

51.915 

42  

51.977 

52.039 

52.100 

52.162 

52.224 

52.285 

52.347 

52.408 

52.470 

52.531 

43  

52.592 

52.653 

52.714 

52.775 

52.836 

fi2.8»7 

w.958 

53.018 

53.079 

53.134 

44  

53.200 

53.26U 

53.321 

53.381 

53.441 

53.501 

53.561 

53.621 

53.681 

53.741 

4)  

53.801 

53.861 

53.921 

53.980 

54.040 

54.099 

54.159 

54.218 

54.277 

54.336 

46  

54.396 

54.455 

54.514 

54.573 

54.632 

54.690 

54.749 

54.808 

54.867 

54.925 

47  

54.984 

55.042 

55.101 

55.159 

55.217 

55.275 

55.334 

55.392 

55.450 

55.508 

48  

55.56H 

55.623 

55.681 

55.739 

55.797 

55.854 

55.912 

55.969 

56.027 

56.084 

49  

56.141 

56.199 

56.256 

56.313 

56.370 

56.427 

56.484 

56.541 

56.598 

56.655 

742 


Miscellaneous  Tables. 


TABLE  LXXXI. 

Table  of  three-halves  (f )  power  of.  number.* 


Head 

in 

.0. 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

feet. 

0... 

0.0000 

0.0316 

0.0894 

0.1643 

0.2530 

0.3536 

0.4648 

0.5857 

0.7155 

0.8538 

1.... 

1.0000 

1.1537 

1.3145 

1.4822 

1.6565 

1.8371 

2.0238 

2.2165 

2.4150 

2.6190 

2  

2.8284 

3.0432 

3.2531 

3.4881 

3.7181 

3.9529 

4.1924 

4.4366 

4.6853 

4.9385 

3.... 

5.1962 

5.4581 

5.7243 

5.9947 

6.2693 

6.5479 

6.8305 

7.1171 

7.4070 

7.7019 

4  

8.0000 

8.3019 

8.6074 

8.9167 

9.2295 

9.5459 

9.8659 

10.1894 

10.5163 

10.8466 

5.... 

11.1803 

11.5174 

11  8578 

12.2015 

12.5485 

12.8986 

13.2520 

13.6086 

13.9682 

14.3311 

6.... 

14.6960 

15.0659 

15.4379 

15.8129 

16.1909 

16.5718 

16.9557 

17.3425 

17.7322 

18.1248 

18.5203 

18.9185 

19.3196 

19.7235 

20.1302 

20.5396 

20.9518 

2i.;«i66 

21.7842 

22.2045 

s'.'.'. 

22.6274 

23.0530 

23.4812 

23.9121 

24  3455 

24.7815 

25.2202 

25.6613 

26.1050 

26.5.123 

9.... 

27.0000 

27.4512 

27.9050 

28.3612 

28.8199 

29.2810 

29.7445 

30.2105 

30.6789 

31.1496 

10.... 

31.6228 

32.0983 

32.5762 

33.0564 

33.5390 

31.0239 

34.5111 

35.0006 

35.4924 

35.9865 

11.... 

36.4829 

36  9815 

37.4824 

37.9855 

38.4908 

38.9984 

39  5082 

40.0202 

40.5343 

41  0507 

1*.... 

41.5692 

42.0910 

42.6128 

43.138s* 

43.6648 

44.1952 

44.7256 

45.2600 

45.7944 

46.3332 

13.... 

4S.8720 

47.4148 

47.9576 

48.5048 

49.0520 

49.6032 

50.1544 

50.7096 

51.2648 

51.*240 

14  

52.3832 

52.9464 

53.5096 

54.0768 

54.6440 

55.2152 

55.7864 

56.3616 

56.  9368 

57.5156 

15.  .  .  . 

58.C944 

58.6776 

59.^608 

59.8472 

60.4336 

61.0244 

61.6152 

62.2096 

62.8040 

63.4020 

16.... 

64.0000 

64.6020 

65.2040 

65.8096 

6B.4152 

67.0244 

67.6336 

68.2464 

H8.S592 

69.4760 

17  

70.0928 

70.7132 

71.3336 

71.9572 

75.5808 

73.2084 

73.H360 

74.4672 

75.0984 

75.7328 

18.... 

76.3672 

77.0056 

77.6440 

78.2856 

78.9272 

79.5724 

80.2176 

80.8684 

81.5152 

82.1672 

19.... 

82.8192 

83.4748 

84  .  1304 

84.7892 

85.4480 

86.1104 

86.7728 

87.43^4 

88.104(1 

88.7732 

20.... 

89.4424 

90.1152 

90.7880 

91.4636 

92.1392 

92.8184 

93.4976 

94.180a 

94.8624 

95.5484 

21.... 

96.2344 

96  9232 

97.6120 

98.3044 

98.9968 

99.6924 

100.3880 

101.0868 

101.7856 

102.4872 

22.... 

103.1883 

103.8940 

104.600S 

105.3076 

106.0160 

106.7276 

107.4392 

108.1540 

108  8688 

109  .58(54 

23.  .  .  . 

110.3040 

111.0248 

111.7456 

112.4700 

113.1944 

113  9216 

114.6488 

115.3788 

116.1088 

116.8420 

24.... 

117.  5752 

118.3128 

119  0496 

119.7876 

1^0.5272 

121.2696 

122.0120 

122.7576 

123.5032 

124.2516 

25.... 

125.0000 

125.7516 

126  5032 

127.2576 

128.0120 

128.7706 

129.5292 

130.2876 

131.0480 

131.8112 

26.... 

132.5744 

133.3408 

134.1072 

134.8764 

135.6456 

136.4180 

13,'  1904 

137.965-2 

188.  7400 

139.5180 

27.... 

140.2960 

141.0768 

I41.a576 

142.6416 

143.4256 

144  2120 

144.9984 

145.7880 

146.5776 

147  3700 

28.... 

148.1624 

148.9572 

149.7520 

150.5500 

151.  34H) 

152.1488 

152.9496 

153.7532 

154.556* 

155.3632 

29.... 

156.1696 

156.9788 

157.7880 

158.6000 

159.4120 

160.2268 

161.0416 

161.858K 

162.6760 

163.4W4 

30.... 

164.3168 

165.1396 

165.9624 

166.7884 

167.6144 

168.4428 

169.2712 

170.1020 

170.9328 

171.7668 

81.... 

172.6008 

173.4372 

174.2736 

175.1128 

175.9520 

176.7940 

177.6360 

178.4804 

179.3-.MH 

180.1720 

32.... 

181.0192 

181.8692 

182.7192 

183.5716 

184.4240 

185.2792 

186.1344 

186.99:iO 

187.8496 

188.7100 

33.... 

189.5701 

1  90.  4336 

191.2968 

192.1624 

93.0280 

193.8960 

194.7640 

195.6318 

19H.5056 

197.3788 

34.... 

198.2520 

199.1460 

200.04dO 

200  9008 

201.7616 

24B.H424 

20:5.5232 

204.4068 

205.29H4 

206.1764 

35.... 

207.0624 

207.9512 

208.8400 

209.7312 

210.6224 

211.5204 

212.4184 

213.3104 

214.2U24 

2:5.1012 

36.... 

216.0000 

216.9012 

217.8024 

218.7060 

219.6096 

220.5760 

221.4224 

222.3312 

223.2400 

224.1512 

37.  .  .  . 

225.0624 

225.976(1 

226.8896 

227.8056 

228.7216 

299.6404 

230.5592 

231.4MX) 

232.40(1* 

233.3244 

38.... 

234.2480 

235.1736 

236.0992 

237.0276 

237.9560 

2*38.8868 

239.8176 

240.7508 

241.^840 

242.6HI6 

39.... 

243.5552 

244.4932 

245.4312 

^46.3712 

247.3112 

248.2540 

249.196S 

250.1420 

251.0S7  2 

252.  OH  18 

40.... 

252.9824 

253.9320 

254.8816 

255.8340  256.7864 

257.7412 

258.6960 

259.6528 

260.KOJ6 

261.  SOS* 

41.... 

262.5280 

263.4896 

264.4512 

265.41521  266  3792 

?R7.345li 

268.3120 

269.2804 

27'0.24H8 

271  2200 

42.... 

272.1912 

273.1644 

274.1316 

275.1132 

276.0888 

277.0672 

278.0456 

279  6252 

2*0.0048 

280.  VJ87  2 

43.... 

281.9696 

282.9544 

283.93*2 

284.^264 

285.9136 

286.9028 

287.8920 

288  8836 

289.8752 

29<l.  S»:  92 

44.... 

291.8632 

292.8597 

293.  a5K 

294.8536 

295.8520 

296.8528 

297  8536 

298.8564 

299.8592 

300.W540 

45.... 

301.8688 

302.8764 

303.8840 

304.8936 

305.9032 

306.9148 

307.9264 

308.9404 

309.9544 

310.9708 

46... 

311.9872 

313.0056 

314.0240 

315.0448 

316.0656 

317.0877 

318.1112 

319.0556 

320.0000 

321.1080 

47.... 

322.2160 

323.2452 

324.2744 

325.3060 

326.3376 

327.3716 

328.4056 

3-29.4416 

3H0.4776 

331.5156 

48  

332.  5536 

333.5927 

334.6383 

335.4753 

336.7188 

337.7588 

338.8051 

349.8529 

840.8972 

341.9479 

49.  ... 

343.00011 

344.0486 

345.0986 

34B.1500 

347.2079 

348.2622 

349.3179 

350.3750 

351.4336 

352.4-8(5 

50.... 

353.55(10 

354.6128 

355.6720 

356.7376 

357.7996 

358  8681 

359.9329 

360.9992 

362.0719 

363.1409 

'From  Water-Supply  and  Irrigation  Paper  No.  IbO. 


Three-Halves  Powers. 


743 


TABLE  LXXXI— Continued. 
Table  of  three-halves  ( I )  power  of  number. 


Head 

in 

.0 

.1 

2 

.3 

.4 

.5 

.6 

^ 

.8 

.9 

feet. 

51... 

364.2114 

365.2832 

366.3564 

367.4311 

368..J020 

369  5794 

370.6582 

371.7*33 

372  8149 

373.8927 

52.... 

374.9772 

376.0578 

377.1397 

378.2331 

379.3078 

380.3940 

381.4815 

382.5708 

383.6606 

384.7522 

M.... 

3&>.8453 

386.9343 

3H8.0301 

389.1219 

390.2205 

391.3150 

392.4163 

393.5136 

394.6122 

395.7122 

54.... 

396.8136 

397.  9163 

399.0204 

40  J.  1258 

401.2326 

402.3408 

403.4448 

404.5557 

405.6679 

406.7759 

55.  .  .  . 

407.8855 

409.0017 

410.1139 

411.2273 

412.3477 

413.4639 

414.5814 

415.7002 

416.8204 

417.9419 

56.  .  .  . 

419.0648 

420.1833 

421.3089 

422.4257 

423.5583 

424.6879 

425.8131 

426.9453 

428.0732 

429.2080 

57.  .  .  . 

430.3386 

431.4704 

432.6036 

433.7380 

434.8738 

436.0110 

437.1494 

438.2892 

439.4302 

440.5726 

58.... 

441.7106 

442.8556 

443.9961 

445.1438 

446.2869 

447.4372 

448.5830 

449.7300 

450.8842 

452.0359 

59.... 

454.0849 

455.3271 

455.4907 

456.6455 

457.8017 

458.9592 

460.1179 

4*1.2720 

462.4334 

463.5960 

60.... 

464.7540 

465.919,' 

467.0797 

468.2475 

469.4106 

470.5750 

471.7467 

472.9J37 

474.0819 

475.2514 

61.... 

476.4222 

477.3942 

478.7676 

479.9422 

481.1181 

482.2891 

483.4676 

484.6473 

485.8222 

487.0044 

62.... 

488.1880 

489.3666 

490.5465 

491.7339 

492.9163 

494.1000 

495.2912 

496.4774 

497.6648 

498.8536 

83.... 

500.0436 

501.2348 

502.4273 

503.6211 

504.8161 

506.  00*51 

507.2036 

508.4024 

509.5961 

510.7974 

64.... 

512.0000 

513.1974 

514.3960 

515.6024 

516.  8035 

518.0059 

519.2160 

520.4209 

521.6270 

522.8344 

(55.  .  .  . 

524.0430 

525.2528 

526.4639 

527.6762 

528.8898 

530.1046 

531  3120 

532.5313 

533.7498 

534.9630 

66.... 

536.1840 

537.2996 

538.6230 

539.8411 

541.0870 

542.2875 

543.5092 

544.7389 

545.9630 

547.18C4 

H7  

548.4151 

549.6429 

550.8720 

552.1022 

553.3337 

554.56r>5 

555.6179 

557.0356 

558.2652 

559.5027 

68.... 

560.7416 

501.974H 

563.2160 

564.4516 

56  >.  6953 

56(5.9334 

568.1795 

r>69.4199 

570.6616 

571.9113 

69.... 

573.1554 

574.4006 

575.6473 

576.8947 

578.1436 

579.3937 

580.6449 

581.8974 

583.1510 

584.4059 

70.... 

585.6620 

586.9122 

588.1707 

589.4303 

590.6841 

591.9462 

593.2023 

594.4668 

595.7253 

596.9921 

71.... 

598.2531 

599.5152 

600.7856 

602.0500 

603.3157 

604.5825 

605.8505 

607.1197 

608.3901 

609.6616 

72.... 

610.9344 

612.2083 

613.4340 

614.7596 

616.0371 

617.3085 

618.5883 

619.8692 

621.0841 

622.4274 

73.... 

623.  71  20 

624.9903 

626.2699 

627.5579 

628.8398 

630.1302 

631.4144 

632.6997 

633.9862 

635.2813 

74.... 

636.5702 

637.8602 

639.1513 

640.4437 

641.7372 

643.0318 

644.3276 

645.6246 

646.9152 

648  2145 

75.... 

649.5150 

6.50.8166 

652.1118 

653.4157 

654.7208 

656.0195 

657.3268 

658.6278 

659.9375 

661.2408 

76  

662.5452 

663.8583 

665.1650 

666.4728 

667.7894 

669.0996 

670.4108 

671.7131 

673.0368 

674.3514 

675.6673 

676.9*42 

677.2043 

679.6216 

680.9419 

682.26&J 

683.5784 

684.9021 

686.2271 

687.5454 

78!!! 

WR.8788 

690.2009 

691.5226 

692.8532 

694.1771 

695.5100 

696.8361 

698.8361 

699.1713 

700.8292 

79.... 

702.1599 

703.4995 

704.8324 

706.1665 

707.5016 

708.8379 

710.1752 

711..  '137 

712.8534 

714.1941 

80.... 

715.5360 

716.8789 

718.2230 

719.5683 

720.9146 

722.2540 

723.602ti 

724.9523 

726.2950 

727.6496 

81.... 

729.0000 

730.3460 

731.7613 

733.0495 

7^4.3989 

735.7575 

737.1091 

738.4699 

739.8237 

741.1876 

742.5340 

743.K998 

745.2580 

746.6173 

747.9776 

749.3392 

750.7018 

752.0655 

753.4303 

754.1962 

83!!! 

756.1632 

757.  53  12 

758.9004 

760.2624 

761.6338 

763.01)63 

764.3798 

765.7461 

767.1219 

768.4904 

84.... 

T.iQ.8684 

771.2474 

772.6192 

774.0004 

775.3743 

776.7493 

778.1338 

779.5110 

780.8892 

782.2770 

85.... 

783.6575 

785.0389 

686.4215 

787.8052 

789.1984 

790.5843 

791.9712 

793.3591 

794.7482 

796.1383 

86.... 

797.5296 

798.9219 

800.3066 

801.7011 

803.0966 

804.4932 

805.8909 

807.2810 

808.680* 

810.0833 

87.  .  .  . 

811.47'51 

812.8781 

814.2736 

815.6788 

817.0763 

818.4837 

819.8834 

821.2929 

822.6947 

824.1064 

88.... 

H25.5704 

826.9154 

828.3-214 

829.7374 

831.1456 

S:«  .V>4<) 

833.9652 

835.3765 

836.7890 

838.2025 

89.... 

839.6171 

S41.  0327 

842.4494 

843.8671 

845.2859 

846.7058 

848.1267 

849.5487 

850.9627 

X52.3868 

90.  .  .  . 

853.8120 

855.2382 

856.6564 

858.0847 

859.5051 

860.9355 

862.3670 

863.7905 

865.2241 

8B6.6496 

91.... 

868.0763 

869.5130 

870.9417 

872.3806 

873.8114 

875.2432 

876.6761 

878.1192 

879.5541 

880.9901 

92.... 

882.4272 

883.8652 

885.3044 

886.7445 

888.1857 

889.6280 

891.0712 

892.5156 

893.9609 

895.4073 

93  

896.8518 

898.3032 

899.7528 

901.1946 

902.6456 

904.09X2 

905.5519 

906.9972 

908.4530 

909.9097 

94.... 

911.3582 

912.8170 

914.2675 

915.7284 

917.1809 

918.643'J 

920.0985 

9-21.5541 

923.0202 

924.4778 

95.... 

925.9365 

927.4056 

928.8664 

930.3281 

931.7908 

933.2642 

934.7290 

936.1948 

937.6616 

939.1295 

98.... 

940.5984 

942.0683 

943.5392 

945.0111 

946.4841 

947.9581 

949.4:131 

950.9091 

952.3764 

953.8545 

97  

955.3336 

956.8136 

958.2948 

959.7672 

961.2503 

962.734-> 

964.2099 

965  6961 

967.1  73^ 

968.6617 

98.... 

970.1412 

971.6314 

973.1129 

974.6051 

976.0886 

977.  582^ 

979.0684 

980.5548 

98-2.0522 

983.5407 

93.  .  .  . 

9&J.0302 

986.5206 

988.0220 

989.5145 

991.0080 

992.51(25 

993.9980 

995.4945 

996.9920 

998.4905 

100 

1  OOO.OUOO 

744 


Miscellaneous  Tables. 


TABLE  LXXXII. 


Table  of  Jive-halves  (|)  powers  of  number*. 


Head 

in 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

feet. 

i 

0  

0  000 

.003 

.018 

.049 

.101    .177 

.279 

.410 

.572 

.768 

1  

1.000 

1.269 

1.578 

1.927 

2.319 

2.756 

3.238 

3.769 

4.347 

4.976 

2  

5.657 

6.390 

7.179 

8.0*2 

8.923 

9.883 

10.90 

11.880 

13.118 

14.320 

3  

15.589 

16.920 

18.317 

19.784 

21.315 

22.918 

24.588 

26.333 

28.150 

30.038 

4  

32.000 

34.038 

36.149 

38.343 

40.612 

42.957 

45.384 

47.888 

50.477 

53.150 

5  

55.901 

58.736 

61.662 

64.671 

67.765 

70.945 

74.211 

77.671 

81.014 

84.553 

6... 

88.182 

91.903 

95.716 

99.622 

103.622 

107.718 

111.910 

116.198 

120.578 

125.063 

7  

129.642 

134.325 

139.104 

149.086 

148.962 

154.050 

159.235 

164.526 

169.915 

175.420 

8  

181.019 

186.729 

192.544 

198.470 

204.506 

210.647 

216.892 

123.251 

229.724 

236.313 

9  

243.000 

249.804 

256.726 

263.757 

270.908 

278.170 

286.452 

293.047 

300.654 

308.385 

10  

316.228 

324.190 

332.275 

340.477 

343.806 

357.252 

365.817 

374.511 

383.314 

392.258 

11... 

401.311 

410.500 

419.798 

429.242 

438.797 

448.477 

458.293 

468.234 

478.301 

488.507 

18  

49H.820 

509.301 

519.879 

530.610 

541.446 

552.438 

563.548 

574.802 

586.163 

597.696 

13  

6U9.336 

621.137 

633.046 

645.170 

657.297  (569.641 

682.094 

694.727 

707.457 

720.354 

14  

733.365 

746.539 

759.842 

773.301 

786.873 

800.618 

814.476 

828.521 

842.668 

856.988 

15  

871.416 

886.038 

900.767 

915.659 

930.684 

945.872 

961.194 

976.697 

992.303 

1008.092 

16  

1024.000 

1040.092 

1056.305 

1072.703 

1089.200 

1105.896 

1122.724 

1139.708 

1156.831 

1174.144 

17  

1191.578 

1209.192 

1226.945 

1244.856 

1262.909 

1281.140 

1299.514 

1318.066 

1336.744 

1355.621 

18  

1374.606 

1393.809 

1413.121 

1432.634 

1452.257 

1472  082 

1492.055 

1512.194 

1532.482 

1552.956 

19  

1573.561 

1594.373 

1615.296 

1636.428 

1657.691 

1679.145 

1700.751 

1722.529 

1744.459 

1766.583 

20  

1788.840 

1811.312 

1833.918 

1856.719 

1879.636 

1902.769 

1926.059 

1949.526 

1973.130 

1996.953 

21  

2020.914 

2045.075 

2069.374 

2093.875 

2118.536 

2143.378 

2168.381 

2193.588 

2218.935 

2244.465 

22  

2270.136 

2296.057 

2322.142 

2348.  3fi8 

2374.758 

2401.380 

2428.121 

2455.096 

2482.213 

2509.519 

23  

2536.992 

2564.678 

2592.507 

2620.551 

2648.740 

2677.167 

2705.716 

2734.482 

2763.394 

2792.524 

24  

282  1.  800 

2851.343 

2881.010 

2910.848 

2940.859 

2971.115 

3001.495 

3032.123 

3062.874 

3093.875 

25  

3125.000 

3156.375 

3187.876 

3219.627 

3251.505 

3283.661 

3315.942 

3348.402 

3381.038 

3413.905 

26.... 

3446.924 

3480.200 

3513.603 

3547.239 

3581.054 

3615.077 

3649.254 

3683.666 

3718.232 

3753.034 

27  

3787.992 

3823.187 

3858.538 

3894.127 

3929.872 

3985.830 

4001.945 

4038.328 

4074.868 

4111.623 

28  

4148.536 

4ia5.692 

4223.006 

4260.565 

4298.283 

4336.247 

4374.370 

4412  711 

4451.242 

4489.991 

29  

4528.930 

4568.089 

4607.410 

4646.980 

4686.713 

4726.697 

4766.843 

4807.212 

4847.745 

4888.530 

30  

4929.510 

4970.714 

5012.052 

5053.676 

5095.466 

5137.512 

5179.693 

5222.131 

5264.736 

5307.600 

31... 
32  

5350.631 
5792.608 

5303.891 
5887.995 

5137.349 
5883.552 

5481  .037  i 
5929.376' 

5524.893 
5075.888 

5569.011 
6021  .568 

5613.298 
6067.  9f,8 

5&57.816 
6114.638 

5702.535 
6161.480 

5747.487 
6208.,  559 

33  6255.810 

6303.365 

6351.060 

6398.995 

6447.135 

6495.516 

6544.070 

6592.899 

6641.903 

6691.148 

34  

6740.568 

6790.879 

6841.368 

6890.904 

6940.613 

6991.149 

7041.896 

7092.923 

7144.092 

7195.542 

35  

7247.170 

7299.080 

7351.168 

7403.504 

7456.019 

750S.960 

7562.081 

7615.167 

7668.432 

7722.126 

3f,  

777rt.OOO 

7830.133 

7884.447 

7939.028 

7993.789 

8051  .024 

8104.060 

8159.555 

8215.232 

8271.179 

37  

8327.309 

8383.709 

8440.293 

8497.149 

8554.188 

8611.515 

8669.026 

8726.796 

8784.750 

8842.995 

3H  

8901.424 

8960.114 

9018.989 

9078.157 

9137.510 

9197.142 

9256.959 

9317.056 

9377.339 

9437.902 

39  

9498  653 

9559.684 

9620.903 

9682.388 

9744.061 

9806.033 

9868.193 

9930.637 

9993.271 

0056.189 

40  

10119.296 

0182.673 

0246.240 

0310.110 

10374.171 

10438.519 

0503.058 

0567.869 

0632.872 

0698.164 

41  

10763.648 

0829.423 

089.",.  389 

0961.648 

11028.099 

11094.842 

1161.779 

1228.993 

1296.340 

1364.118 

4-.'  

11432.030 

1502.221 

1568.607 

1637.288 

11706.165 

11775.356 

1844.743 

1939.996 

1984.205 

2054.351 

43  

12124.693 

2195.835 

2266.173 

2337.313 

12408.650 

12480.272 

2552.091 

2624.213 

2696.634 

2769.197 

44  .... 

12841.761 

2915.113 

2988.340 

3062.014 

13135.829 

13209.950 

3284.271 

3358.8*1 

3433.692 

3508.794 

45  

13584.096 

3659.726 

3735.557 

3811.680 

13888.005 

13964.623 

4041.444 

4118.576 

4195.912 

4273.560 

46  

14351.411 

4429.558 

4507.909 

4-86.574 

14665.444 

14744.578 

4823.982 

4899.897 

4976.000 

5059.  C65 

47  

15144.152 

5224.849 

5305.752 

5386.974 

15468.402 

15550.151 

5632.107 

5714.?64 

5796.829 

5879.597 

48  

15962.573 

6045.809 

6129.325 

6203.457 

16297.190 

16381.302 

64H5.928 

65*2.036 

6635.7^3 

6722.212 

49  
50. 

16807.000 
17677.500 

6892.786 

6978.851 

7065.195 

17152.070 

17238.979 

7326.168 

7413.647 

7501.893 

7589.181 

1 

Relation  of  Rainfall  to  Stream  Flow.  745 


TABLE  LXXXIIL 

Showing  relation  of  mean  rainfall  to  the  maximum  and  minimum  discharge 

of  various  rivers. 

DRAINAGE  AREA,  500  TO  1,000  SQUARE  MILES 

Drainage    Mean  Annual     Discharge  Ca  Ft 

STREAM  AND  LOCALITY.  Area,  Rainfall,                  pef  Sec. 

Sq.  Miles  Inches  per  Sq.  Mile 

I.  AMERICAN  STREAMS.  MAX.  Mw. 

Broad  river  at  Carlton,  Ga 762  47.73        22.21         .394 

Coosawattee  river  at  Carters,  Ga 532  52.73        15.17         .588 

Des  Plaines  river  at  Riverside,  111 630  29.75         14.23         .000 

Etowah  river  at  Canton,  Ga 604  52.73        31.50         .405 

Flint  river  at  Molina,  Ga 892  52.73          7.37         .062 

French  Broad  river  at  Asheville,  N.  C 987  7 . S8         .660 

Greenbriar  river,  mouth  Howard's  cr.,  W.  Va.  810  40.70                          .120 

Housatonic  river,  Massachusetts 790  . 165 

Little  Tennessee  river  at  Judson,  N.  C 675  56.40         .408 

Mahoning  river  at  Warren,*  0 596  .017 

Mahoning  river 967  .026 

Monocacy  river  at  Frederick,  ,Md 665  38.77        16.98         .116 

North  river  at  Port  Republic,  Va 804  38.77        29.78         .220 

North  river  at  Glasgow,  Va... 831  38.77        44.80         .180 

Olentangy  river  at  Columbus,  0 523  .014 

Passaic  river  at  Paterson,  N.  J 791  45.00                           .190 

Potomac  river,  no.  branch  at  Cumberland,  Md.  891  38.77        22.82         .045 

Potomac  river  at  Cumberland,  Md 920  38.77         19.46         .022 

Raritan  river  at  Bound  Brook,  N.  J ,  879  45.94         59.30         .140 

Schoharie  creek  at  Fort  Hunter,  N.  Y 948  39.25         44.00 

Shenandoah  river  at  Fort  Republic,  Va 770  38.77                          .167 

Tuckasagee  river  at  Bryson,  N.  C 662  45.30         .603 

II.  FRENCH  STREAMS. 

Armancon  river  at  Aisy 575  49.20         .011 

Armancon  river  at  Tonnerre 853  .034 

Marne  river  at  St.  Pizier 915  30.70           7.73         .101 

Meuse  river  at  Pagny-la-Blanchecote 573  .039 

Meuse  river  at  Chalaines 607  31.51                           .041 

Meuse  river  at  Pagny-sur-Meuse 734  .056 

Meuse  river  at  Vignot 817  .085 

Meuse  river  at  Mt.  Mihiel 914  .078 

III.  GERMAN  STREAMS. 

Ihna  river  at  Stargard 672  26.60        15.50         .137 

Jagst  river  at  its  mouth 708  29.50                           .200 

Kocher  river  at  its  mouth   - 768  29.50                           .221 

Lippe  river  at  Hamm 965  9.75         .235 

Malapane  river  at  Czarnowanz 773  25 . 04         14  35         .274 

Oppa  river  at  Strebowitz 805  24.40         21.95         .256 

Stober  river  at  its  mouth..  620  22.70          3. 05 


*From  paper  on  Water  Supply  for  New  York  State  Canals,  Report  of  State 
Engineer  on  Barge  Canal,  1901. 


746  Miscellaneous  Tables. 


TABLE  LXXXIIL-Continued. 
DRAINAGE  AREA,  1,000  TO  2,500  SQUARE  MILES. 

Drainage    Mean  Annual     Discharge  Cu.  Ft. 


STREAM  AND  LOCALITY. 

Area, 

Rainfall, 

per  Sec. 

Sq.  Mile. 

Inches 

per  Sq.  M 

lie. 

I.     AMERICAN  STREAMS. 

MAY. 

MIN. 

Androscoggin  river  at  Rumford  Falls,  Me.  .  . 
Broad   river  at  Gaffney,  S.  C  

2,220 
1,435 

40.39 
47.73 

25.00 
13.05 

.475 
.550 

Catawba  river  at  Catawba,  N  .  C  .  

1,535 

34.30 

.553 

Chattahoochee  river  at  Oakdale,  Ga  

1,560 

48.91 

21.75 

.432 

Genesee  river  at  Mt.  Morris,  N.  Y  

1,070 

38.09 

39.20 

.094 

Greenbriar  river  at  Aederson,  W.  Va  

1,344 

44.86 

41.55 

.041 

James  river  at  Buchanan,  Va  

2,058 

40.83 

15  56 

.146 

Neuse  river  at  Raleigh,  N.  C  

1,000 

.193 

Neuse  river  at  Selma,  N.  C  

1,175 

6.70 

.064 

2,425 

49.23 

14.92 

.157 

Oconee  river  at  Carey,  Ga  

1,346 

49.31 

7.44 

.283 

Oostannala  river  at  Resaca,  Ga  

1,527 

52.47 

14.50 

.389 

Potomac  river  at  Cumberland,  Md  

1,364 

35.28 

.018 

Saluda  river  at  Waterloo,  S.  C  

1,056 

12.08 

.275 

Schuylkill  river  at  Philadelphia,  Pa  

1,800 

.170 

Schuylkill  river  at  Fairmount,  Pa  

1,915 

12.17 

.013 

Scioto  river  at  Columbus,  O  

1,07.0 

.004 

Scioto  river  at  Shadeville,  O  

1,670 

.015 

Tar  river  at  Tarboro,  N.  C  

2,290 

6.38 

.074 

Youghiogheny  river  at  Ohio  Pyle,  Pa   

1,775 

.060 

II.     FRENCH  STREAMS. 

Aisne  river  at  Biermes  

1,341 

- 

.085 

Aisne  river  at  Berry-au-Bac  

2,120 

.092 

Aisne  river  at  Berry-au-Bac  

2,120 

7.58 

Loing  river  at  its  junction  with  the  Seine.  .  ^ 

1,785 

28.40 

.046 

Lys  river  ,  

1,420 

1.74 

.099 

Marne  river  -at  La  Chaussee  

2,297 

.010 

Marne  river  at  Chalons  

2,497 

.010 

Meuse  river  at  Verdun  

1,219 

28.33 

.110 

Oise  river  at  Chauny  

1,575 

.-104 

Seine  river  at  Troyes  

1,314 

.051 

III.     GERMAN  STREAMS. 

Bober  river  at  Sagan  

1,638 

39.20 

17.40 

.389 

Drage  river  at  its  mouth  

1,234 

2.11 

.356 

Ill  river  at  Strasburg  

1,294 

9.15 

.327 

Kuddow  river  at  Usch  

1,830 

18.90 

19.30 

.405 

Lahn  river  at  Diez  

2,008 

25.60 

12  80 

.123 

Lippe  river  at  Wesel  

1,890 

11.62 

.198 

Main  river  above  mouth  of  the  Regnitz  river 

1,725 

27.44 

.224 

Netze  river  at  Antonsdorf  

1,086 

.063 

Netze  river  above  Eicbhorst  

1,130 

.046 

Oder  river  at  Hoschialkowitz  

1,440 

21.60 

.155 

Oder  river  at  Annaberg  

1,800 

24.60 

27.00 

.219 

Oder  river  at  Olsau  

2,250 

24.60 

43.90 

.274 

Obra  river  at  Moschin  

1,325 

.101 

Ruhu  river  at  Mulheim  

1,728 

33.80 

.176 

Saale  river  at  its  junction  with  the  Main  

1,070 

27.76 

.081 

Welna  river  at  Kowanowko,  near  mouth  .  .  . 

1,013 

3.14 

.077 

Relation  of  Rainfall  to  Stream   Flow. 


747 


TABLE  LXXX1IL—  Continued. 


DRAINAGE  AREA,  2,500  TO  5,000  SQUARE  MILES. 


Drainage    Mean  Annual    Discharge  Cii.  Ft. 

STREAM  AND  LOCALITY. 

Area, 

Rainfall, 

per  Sec 

Sq.  Miles. 

Inches. 

per  Sq.  Mi 

ile. 

I.     AMERICAN  STREAMS. 

MAX. 

Mi*. 

Black  Warrior  river  at  Tuscaloosa,  Ala.  .  .  . 

4,900 

38.80 

.018 

Broad  river  at  Alston,  S.  C  r 

4,609 

10.26 

.394 

Cape  Fear  river  at  Fayetteville,  W.  Va  

4,493 

1.17 

.076 

Catawba  river  at  Rock  Hill,  S.  C  

2,987 

21.96 

.445 

Chattahoochee  river  at  West  Point,  Ga.  .  .  . 

3,300 

52.92 

17.37 

.252 

Connecticut  river  at  Dartmouth,  N.  H  

3,287 

.306 

Coosa  river  at  Rome,  Ga  

4,001 

52.73 

11.42 

.225 

Crow  Wing  river,  Minnesota  

3576 

30.84 

2.84 

.250 

Dan  river  at  Clarksville,  Va  

3,749 

38.28 

8.80 

.107 

Hudson  river  at  Mechanicsville,  N.  Y  

4,500 

41.61 

15.50 

.189 

Kennebec  river  at  Waterville,  Me  

4,410 

25.20 

.006 

4,085 

19.83 

.310 

*Merrimac  river  at  Lawrence,  Mass  

4,551 

20.00 

.27 

Mohawk  river  at  Rexford  Flats,  N.  Y  

3,384 

23.10 

Mohawk  river  at  Cohoes,  N.  Y.  

3,444 

38.65 

.232 

Ocanee  river  at  Dublin,  Ga  

4,182 

49.31 

6.69 

.021 

Potomac  river  at  Dam  No.  5,  Md  

4,640 

38.77 

22.15 

.078 

Savannah  river  at  Calhoun  Falls,  Ga   

2,712 

47.73 

.96 

.518 

Shenandoah  river  at  Millville,  W.  Va   

2,995 

39.56 

11.44 

.203 

Staunton  river  at  Clarksville,  Va  

3,546 

38.28 

10.30 

.157 

Susquehanna  river,  w.  br.,  Williamsport.Pa. 

4,500 

11.60 

.178 

Tallapoosa  river  at  Milstead,  Ala  

3,840 

9.50 

.091 

Yadkin  river  at  Salisbury,  N.  C  

3,399 

23.55 

.225 

Yadkin  river  at  Norwood,  N.  C  

4,614 

13.70 

.284 

II.     FRENCH  STREAMS. 

Aisne  river  at  Soissons  

3,040 

6.43 

.081 

Aisne  river,  above  junction  with  the  Oise  rivei 

3,285 

23.50 

5.95 

.096 

Eure  rivei*  at  its  mouth  

2,980 

22.30 

2.72 

.076 

Isere  river  at  its  mouth  

•    4,300 

21.00 

.780 

Marne  river  at  Chateau  Thierry  

3,333 

.127 

Meuse  river  at  Sedan  

2,560 

28.33 

8.05 

.194 

Meuse  river  at  Fumay  

3,700 

28.33 

4.04 

.191 

Seine  river  at  Bray  

3,750 

4.05 

.003 

Seine  river  at  Nogent-sur-Seine  

3,594 

.103 

Yonne  river  at  Sens  

4,270 

9.09 

.106 

Yonne  river  at  Nogent-sur-Seine  -. 

4,300 

30.80 

6.37 

.140 

III.     GERMAN  STREAMS. 

Main  river,  below  mouth  of  the  Regnitz  river 

4,650 

27.44 

.186 

3  550 

29.48 

14.92 

.199 

Mur  river  at  Graz   

2,959 

12.98 

.243 

Neckar  river  at  Heilbronn  ,  

3,155 

.146 

Neckar  river  at  Offenau  

4,770 

33.35 

.167 

Oder  river  at  Ratibor  

2,580 

S4.60 

21.20 

.306 

Oder  river  at  Kosel  

3  520 

24.60 

14.10 

.128 

Oder  river  at  Krappitz  

4,150 

24.60 

3.86 

.187 

Regnitz  river  at  its  juhc.  with  the  Main  river 

2,920 

25.60 

.164 

•'"Figurrs  supplied  by  Mr.  Rich.  A.  Hale,  Lawrence.  Mass. 

748  Miscellaneous  Tables. 

TABLE  LXXXIII.- Continued. 
DRAINAGE  AREA,  5,000  AND  OVER  SQUARE  MILES. 


Drainage  Mean  Annual 

Discnarge  Cu.  Ft. 

STREAM  AND  LOCALITY. 

Area, 

Rainfall, 

per  Sec. 

Sq.  Miles. 

Inches. 

per  Sq.  Mile. 

I.     AMERICAN  STREAMS. 

MAX. 

MlN. 

Connecticut  river  at  Holyoke,  Mass  

8,660 

13.26 

.029 

Connecticut  river  at  Hartford,  Conn  

10,234 

44.53 

.310 

Connecticut  river  at  Hartford,  Conn  

10,234 

44.53 

20.27 

.510 

Coosa  river  at  Riverside,  Ala  

6,850 

48.08 

10.53 

.197 

Delaware  river,  New  Jersey  

6,750 

50.00 

.300 

Delaware  river  at  Stockton,  N.  J  

6,790 

45.29 

37.50 

.170 

Delaware  river  at  Lambertsville,  N.  J  

6,855 

45.29 

9.71 

.364 

James  river  at  Richmond,  Va  

6,800 

40.83 

.191 

Kanawha  river  at  Charleston,  W.  Va  

8,900 

40.70 

13.49 

.123 

Mississippi  river  

7,283 

32.64 

1.49 

.261 

36,085 

25.75 

19.73 

.045 

Mississippi  river  

164,534 

.190 

Mississippi  river  

526,500 

.050 

Mississippi  river  1 

,214,000 

.210 

Missouri  river  

17,615 

15.70 

.100 

New  river  at  Fayette.  W.  Va  

6,200 

40.70 

13.49 

.189 

Ohio  river  at  Pittsburg,  Pa  

19,990 

.114 

Ohio  river  

200,000 

41.50 

.270 

Os.wego  river  at  Oswego,  N.  Y  

5,013 

37.69 

•230 

Potomac  river  at  Point  of  Rocks,  Md  

9,654 

39.35 

19.40 

,083 

Potomac  river  

11,043 

38.77 

42.60 

.170 

Potomac  river  at  Georgetown,  D.  C  

11,124 

38.77 

15.70 

Potomac  river  at  Great  Falls,  Md  

11,427 

45.36 

41.15 

•215 

Potomac  river  at  Great  Falls,  Md  

11,476 

45.36 

15:25 

.093 

Potomac  river  at  Chain  Bridge,  D.  C  

11,545 

38.77 

17.16 

.165 

Red  river,  Arkansas  

97,000 

39.00 

2.32 

Roanoke  river  at  Neal,  N.  C         

8,717 

38.21 

7.38 

,229 

St.  Croix  river,  Minnesota  

5,950 

32.58 

6.00 

,424 

Savannah  river  at  Augusta,  Ga  

7,294 

47.73 

42.50 

272 

Susquehanna,  w.  branch,  at  Northumberland 

6,800 

17.53 

,074 

Susquehanna  river  at  Harrisburg,  Pa  

.24,030 

18.88 

.092 

Tennessee  river  at  Chattanooga,  Tenn  

21,418 

20.78 

.199 

II.     FRENCH  STREAMS. 

Loire  river  at  Nevers  

6,560 

23.10 

070 

Loire  river,  between  Maine  and  Vienne  rivers 

9,950 

255 

Marne  river  at  Charenton  

5,657 

016 

Marne  river  at  its  junction  with  the  Seine.  .  . 

5,295 

30.70 

4.67       | 

.080 

Meuse  river  at  Maestricht  

8,240 

42.50 

5.51        , 

146 

Meuse  river  at  Maeseyck  

8,480 

42.50 

7.36 

244 

Meuse  river  above  Ruremond  

8,750 

3.01 

317 

Oise  river  at  Creil  

5  622 

3  14 

194 

Rhone  river  at  Lyons  

18,000 

36.32 

11.83 

333 

Seine  river  at  Port  a  1'  Anglais  

17,624 

046 

Seine  river  at  Paris  

20,000 

21.27 

5.80 

085 

Seine  river  at  Mantes  

25,135 

3.09 

091 

Seine  river  at  mouth  of  the  Eure  river..  . 

28  583 

3  09 

III.     GERMAN  STREAMS. 

Elbe  river  at  Torgau  

22,000 

27.09 

2.89 

144 

Main  river  above  mouth  of  Saale  river 

5  820 

18° 

Main  river  below  mouth  of  Saale  river 

6,900 

166 

Main  river  above  mouth  of  Tauber  river 

7,290 

167 

Main  river  below  mouth  of  Tauber  river 

8,000 

167 

Main  river  at  Frankfort.  .  . 

9,610 

12.50 

1^1 

Memel  river  art  Tilsit  

38,600 

4  02 

813 

Moselle  river  at  Kochem. 

10,253 

8  52 

174 

Moselle  river  at  Coblenz 

10,840 

24.76 

13.04 

.166 

Relation  of  Rainfall  to  Stream  Flow.  749 


TABLE  LXXXIII. -Continued. 
DRAINAGE  AREA,  5,000  AND  OVER  SQUARE  MILES. 

Drainage  Mean  Annual  Discharge  Cu.  Ft 

STREAM  AND  LOCALITY                              Area  Rainfall  Per  Sec. 

Sq.  Miles.  Inches.  Per  S*q.  Mile, 

III.     GERMAN  STREAMS.  MAX.  MIN. 

Neckar  river  at  Heidelberg 5,321  32. 17         .215 

Neckar  river  at  Mannheim 5,395  31.02 

Oder  river  at  Ohlau 7,750  24.60  4.17         .215 

Oder  river  at  Breslau,  below  the  Ohle  river.        8,330  24.60  10.40         .209 

Oder  river  at  Steinau 11,412  24.02  .95         .229 

Oder  river  below  mouth  of  the  Warthe  river      28,319  23.62  .61         .212 

Saale  river  at  Rothenburg 7,282  27.76  5.41         .120 

Warthe  river  at  Pogorzelice ...        7,900  .164 

Warthe  river  at  Posen 9,620  6.37         .100 

Warthe  river  at  Landsberg t        20, 020  21 . 65  2 . 56         .192 


750 


Miscellaneous  Tables. 


TABLE  LXXXIV. 

Mean  average  rainfall,  run-off,  and  evaporation  for  storage,  growing  and  re- 
plenishing periods  for  12  streams  of  the  United  States.* 


Period. 

Muskingum  River, 
from    1888   to  1895, 
eight  years.  Catch- 
ment area,  5,828 
square  miles. 

Genesee  River,  from 
1890  to    1898.   nine 
years.    Catchment 
area,    1,070   square 
toiles. 

Croton    River,    from 
1877  to  1899,  twenty- 
three  years.    Catch- 
ment   area,    338.8 
square  miles. 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

Storage 

18.8 
11.6 
9.3 

9.6 
1.7 
1.8 

9.2 
9.-9 

7.5 

19.4 
11.5 
9.4 

10,5 
1.7 
2.0 

8.9 
9.8 
7.4 

23.7 
13.6 
12.1 

16.8 
2.6 
3.4 

6.9 
11.0 

8.7 

Growing 

Replenishing 

Year  

39.7 

13.1 

26.6 

40.3 

14.2 

26.1 

49.4 

22.8 

26.6 

Period. 

Lake  Cochituate, 
from  1863  to  1900, 
thirty-eight  years. 
Catchment   area, 
18.9  square  miles. 

Sttdbu 
18751 
six  3 
men 
squa 

Rain. 

ry  River,  from 
o  1900,  twenty  - 
rears.    Catch- 
,t  area,   78.2 
re  miles. 

Mystic   Lake,  from 
1878  to  1895,  eighteen 
years.    Catchment 
area,   26.9   square 
miles. 

Rain. 

•sg- 

Evap- 
ora- 
tion. 

Run- 
off. 

Evap- 
ora- 
tion. 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

7.3 

8.6 

8.2 

Storage  

23.1 
11.6 
12.4 

14.9 
2.1 
3.3 

8.2 
9.5 
9.1 

23.6 
10.7 
11.9 

17.9 
1.7 
3,0 

5.6 
fl.O 

8.9 

22.4 
10.9 

10.8 

15.1 
2.8 
2.6 

Growing  

Replenishing  

Year  

47.1 

20.3 

26.8 

46.1 

22.6 

23.5 

44.1 

20.0 

24.1 

Period. 

Neshaminy   Creek, 
from!884to  1899,  six- 
teen years.    Catch- 
ment  area,  139.3 
square  miles. 

Perkiomen   Creek, 
from  1884  to  1899,  six- 
teen years.    Catch- 
in  e  n  t    area,    152 
square  miles. 

Tohickon  Creek,  from 
1884  to  1898,  fifteen 
years.    Catchment 
area,    102.2    square 
miles. 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

Storage  

23.1 
13.4 
11.1 

17.2 
2.7 

!! 

5.9 
10.7 
7.9 

23.2 

13.7 
11.1 

16.7 
3.1 

3.8 

6.5 
10.6 
7.3 

24.2 

14.6 
11.3 

20.5 
3.5 
4.4 

3.7 
1L1 

6.9 

Growing  

Replenishing  ;  

Year  

47.6 

23.1 

24.5 

48.0 

23.6 

24.4 

50.1 

38.4  i        21.7 

Period. 

Hudson  River,  from 
1888   to  1901,    four- 
teen years.    Catch- 
ment    area,     4,500 
square  miles. 

Pequannock     River, 
from    1891  to   1899, 
nine  years.    Catch- 
ment    area,     33.7 
square  miles. 

Connecticut     River, 
from    1872    to     18«5, 
eleven       years. 
Catchment      area, 
10,234  square  miles. 

Rain. 

Run 
off. 

Evap- 
ora- 
tion. 

4.5 
9.2 

7.2 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

Rain. 

Run- 
off. 

Evap- 
ora- 
tion. 

Storage 

20.6 
12.7 
10.9 

16.1 
3.5 
3.7 

33.0 
12.7 
11.1 

19.7 
3.1 
4.0 

3.3 
9.6 
7.1 

18.9 
13.8 
10.3 

15.1 
3.3 
3.6 

3.8 
10.5 
6.7 

Growing 

Replenishing  
Year  .... 

44.2 

23.3 

20.9 

46.8 

26.8 

20.0 

43.0 

22,0 

21.0 

*From  W.  p.  and  I.  Pap?r  No.  so.  Rafter. 


Rainfall,  Run-off  and  Evaporation. 


TABLE  LXXXV— Croton  River,  1868-1899,  inclusive. 
L  Catchment  area=-338,8  square  miles.] 


1868. 

1869. 

1870. 

Period. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Storage 

23.24 

17  25 

5  99 

21  89 

15  75 

6  14 

28  42 

19  01 

9  41 

Growing 

13.64 

5  75 

7  89 

7  77 

2  01 

5  76 

10  59 

1  56 

9  03 

Replenishing1 

14.85 

11  06 

3  79 

15  09 

4  39 

10  70 

10  09 

96 

9  13 

Year  

51.78 

34.06 

17  67 

44.75 

22  15 

22  60 

49  10 

21  53 

27  57 

1871. 

1872. 

1873. 

Storage 

19.83 

9  72 

10  11 

14  57 

10  31 

4  26 

22  19 

18  52 

3  67 

Growing.  

16.04 

2.61 

13.43 

14.33 

3.01 

11  32 

8  65 

1  54 

7  11 

Beplen  i  sh  in  g 

11  95 

5  65 

6  30 

10  75 

4  38 

6  37 

12  58 

3  20 

9  38 

Year 

47  82 

17  98 

29  84 

39  65 

17  70 

21  95 

43  42 

23  26 

20  16 

1874. 

1875. 

1876. 

Storage 

23.74 

22.86 

0.88 

17  10 

14  81 

2  29 

22  64 

19  89 

2  75 

Growing 

12.30 

2.77 

9  53 

16  45 

5  86 

10  59 

7  14 

1  07 

6  07 

Replenishing 

8.68 

1  60 

7  08 

10  33 

3  41 

6  92 

10  11 

1  35 

8  76 

Year 

44.72 

27.23 

17  49 

43  88 

24  08 

19  80 

39  89 

22  31 

17  58 

1877. 

1878., 

1879. 

Storage   .  . 

17.49 

12.36 

5.13 

20.99 

14.19 

6  80 

25.17 

20  81 

4  36 

Growing 

13.17 

.96 

12.21 

11.29 

2  57 

8  72 

18  09 

2  63 

15  46 

Replenishing 

18.46 

5  49 

12.97 

16.72 

5  01 

11  71 

6  96 

1  88 

5  08 

Year  

49.12 

18.81 

30.31 

49.00 

21.77 

27  23 

50  22 

25  32 

24  90 

1880. 

1881. 

1882. 

Storage                           

19.78 

12.19 

7.59 

24.53 

14  79 

9  74 

27  91 

16  85 

11  06 

Growing  • 

11.42 

.68 

10.74 

9  61 

1  95 

7  66 

9  03 

2/06 

6  97 

Replenishing               .  . 

7.57 

.84 

6.73 

8  96 

97 

7  99 

19  10 

6  21 

12  89 

Year  

38.77 

13.71 

25.06 

43.10 

17.71 

25  39 

56  04 

25  12 

30  92 

1883. 

1884. 

1865. 

Stora  go     .  ..  .  .. 

19.03 

11.37 

7.66 

24.81 

16  85 

7  96 

21  86 

15  36 

6  50 

-Growing.  .  .  .. 

12.10 

1.09 

11.01 

15.72 

2  34 

13  38 

12  89 

88 

12  01 

•Replenishing        

10.41 

1.28 

9.13 

8.01 

1  87 

6  14 

12  23 

2  92 

9  31 

Year 

41  54 

13  74 

27  80 

48  54 

21  06 

27  48 

46  98 

19  16 

27  82 

1886. 

1887. 

1888. 

Storage 

25  45 

18.16 

7.29 

23  05 

16  44 

6  61 

30  33 

21  74 

8  59 

Growing 

11  68 

1  53 

10  15 

24  76 

6  71 

18  1)4 

11  25 

2  63 

8  62 

Replenishing 

9  82 

1  23 

8  59 

7  78 

2  60 

5  18 

18  76 

8  23 

10  53 

Year  

46  95 

20.92 

26  08 

55  58 

25  75 

29  83 

60  34 

32  60 

27.74 

752 


Miscellaneous  Tables. 
TABLE  LXXXV— Continued. — Croton  River,  1868-1899,  inclusive. 


Period. 

1889. 

law. 

1891. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run_- 
off. 

Evapo- 
ration. 

Storage                          -  -- 

22.40 
17.37 
18.83 

16.86 
6.49 
8.70 

5.54- 
10.88 
10.13 

25.31 
13.31 
14.60 

19.10 
2.51 

7.02 

6.21 
10.80 

7.68 

26.66 
11.26 

7.78 

21.22 
1.14 
1.11 

5.44 
10.12 
6.67 

Replenishing  

Year  r 

58.60 

32.05 

26.55 

53.22 

28.63 

24.59 

46.70 

23.47 

22.23 

1892. 

1893. 

1894. 

Storage 

22.93 
15.37 
10.30 

12.87 
2.60 
2.31 

10.06 
12.77 
7.99 

27.34 
12.39 
11.08 

21.41 
1.84 
3.51 

6.93 
10.56 

7.67 

23.24 
7.96 
17.06 

15.65 
1.88 
4.41 

7.60 
6.18 
12.64 

Growing 

Replenishing 

Year  

48.60 

17.78 

30.82 

50.81 

26.76 

24.06 

48.24 

21.88 

26,,% 

1895. 

1896. 

1897. 

Storage  

19.55 
11.19 
9.54 

14.78 
1.06 
1.27 

4.77 
10.14 
8.27 

23.18 

24.84 
12.25 
11.27 

18.01 
2.03 
3.13 

6.88 
10.22 
8.14 

20.55 
20.79 
8.76 

14.64 
6.93 
2.78 

6.91 
13.86 
6.08 

25.80 

Growing       

Replenishing      

Year 

40.28 

17.10 

48.36 

23.17 

25.  W 

50.10 

24.30 

1898. 

1899. 

Storage 

28.81 
17.17 
13.36 

20.08 
4.83 
3.99 

8.73 
12.34 
9.37 

22.66 
12.19 
10.37 

21,38 
1.67 
1.96 

1.2ft 
10.02 
8.41 

Growing 

Replenishing  

Year 

59.34 

28.90 

30.44 

45.22 

24.91 

20.31 

Mean  1868-1876,  in- 
clusive. 

Mean  1877-1899,  in- 
clusive. 

Storage            .               

21.51 
11.88 
11.61 

16.46 
2.91 

4.00 

5.05 
8.97 
^T.61 

28.68 
13.68 
12.08 

16.83 
2.57 
3.42 

C.85 
11.01 

8.66 

Growing                    --  

Replenishing      

Year                         

45.00 

23.37 

21.63 

49.33 

22.81 

26.52 

Rainfall,  Run-off  and  Evaporation. 


753 


TABLE  LXXXVI— Lake  Cochituate,  1863-1900,  inclusive. 
[Catchment  area=18.9  square  miles,  not  including  catchment  of  Dudley  Pond.] 


1863. 

1864. 

1865. 

Period.  * 

Rain 
fall. 

Run 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Storage 

29.49 

16.31 

13.18 

24.  70 

14.44 

10.26 

29.  63 

17.28 

12.35 

Growing 

21.71 

5.15 

16  56 

5.20 

1.58 

3.62 

7.37 

1.27 

6.10 

R  eplenishing 

16  49 

5  25 

11  24 

13.47 

3.17 

10.30 

13.43 

2.15 

11.28 

Year          * 

67  69 

26  "71 

40  98 

43  37 

19  19 

24  18 

50  43 

20  70 

29  73 

1866. 

1867. 

1868. 

Storage  

22.87 

9.38 

13.49 

27.02 

16.47 

10.55 

23.02 

16.95 

6.07 

Growing  

22.13 

2.94 

19.19 

•:20.67 

3.34 

17.33 

12.49 

8.22 

9c27 

Replenishing  

16.  31 

3.26 

13.05 

10.98 

2.43 

8.55 

15.65 

4.76 

10.89 

Year 

61  31 

15  58 

45  73 

58  67 

22  44 

36  43 

51  16 

24  93 

26  23 

. 

1869. 

1870. 

1871. 

Storage.               .. 

28.91 

12.83 

16.08 

36.50 

23.72 

12.78 

19.77 

10.19 

9  58 

Growing 

8.65 

2.39 

6.26 

9.18 

1.91 

7.27 

11.72 

2.15 

9  57 

Replenishin  g 

21.25 

4.77 

16.48 

13.00 

2.85 

10.15 

13.  85 

2  38 

11  47 

Year         

58.81 

19.99 

38.82 

68.68 

28.48 

30.20 

45.34 

14.72 

dO  62 

1872. 

1873. 

1874. 

Storage 

14.51 

8.88 

5.63 

20.00 

18.51 

1.49 

20.76 

16  23 

4  53 

Growing 

19.58 

2.95 

16.63 

11.63 

2.47 

9.16 

12  78 

3  83 

8  95 

Replenishing  -               * 

14.20 

6.39 

8.81 

13.27 

4.68 

8.59 

4  64 

1  63 

8  01 

Year       

48.29 

17.22 

31.07 

44.90 

25.66 

19/24 

38.18 

21.69 

16.49 

1875. 

1876. 

1877. 

Storage 

17.80 

10.76 

7.04 

20.45 

14.91 

5.54 

21.61 

15.65 

5  96 

Growing 

15.34 

2  35 

12.99 

13.28 

1.64 

11.64 

8.76 

2.24 

6  52 

Replenishing 

13  11 

3.75 

9.36 

12.57 

3.22 

9.35 

15.54 

4  31 

11  23 

Year 

46.25 

16.86 

29.39 

46.30 

19.77 

26.53 

45.91 

22.20 

23  71 

1878. 

1879. 

1880. 

Storage 

23.38 

19.08 

4.30 

19.96 

16.83 

3.13 

18.47 

8.55 

9  92 

Growing 

13.74 

2.07 

11.67 

13.95 

2.05 

11.90 

12.06 

.62 

11  44 

Replenishing 

12.36 

3.09 

9.27 

5.62 

1.93 

3.69 

6.34 

1.56 

4  78 

Year  

49.48 

24.24 

25.24 

39.53 

20.81 

18.72 

36.87 

10.73 

26.14 

1881. 

1882. 

1883. 

Storage     

22.23 

12.74 

9.49 

23.10 

12.39 

10.71 

16.62 

8.31 

8.31 

Growing     

8.74 

1.56 

7.18 

6.50 

.75 

5.75 

5.08 

.16 

4.92 

Replenishing  .  

8.85 

1.25 

'7.60 

12.35 

2.39 

9.96 

8.53 

1.62 

6.91 

Year 

39  82 

15  55 

24  27 

41  95 

15  53 

26  42 

30  23 

10  09 

20  14 

46 


754 


Miscellaneous  Tables. 


TABLE  LXXXVL— Continued.—  Lake  Cochituate,  1863-1900,  inclusive. 


Period. 

1884. 

1885. 

1886. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration . 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Storage 

24.79 
12.79 
5.82 

15.70 

1.54 
1.09 

9.09 
11.25 
4.73 

22.80 
11.70 
12.15 

11.90 
.76 
3.09 

10.90 
10.94 
9.06 

24.14 
8.26 
11.12 

18.97 
.57 
1.92 

5.17 
7.69 
9.20 

Growing 

Replenishing 

Year  . 

43.40 

18.33 

25.07 

46.65 

15.75 

30.90 

43.52 

21.46 

22.06 

1887. 

1888. 

1889. 

Storage 

26.97 
10.05 
6.53 

19.91 
2.87 
1.83 

7.06 
7.18 
4.70 

24.22 
10.06 
20.79 

15.44 
1.94 
9.09 

8.78 
8.12 
11.70 

21.79 
16.84 
14.56 

17.26 
6.24 

6.65 

4.53 
10.60 
7.91 

Growing 

Replenishing  T  

Year  ,.... 

43.55 

24.61 

18.94 

55.07 

.26.47 

28.60 

53.19 

30.15 

23.04 

1890. 

1891. 

1892. 

Storage 

23.42 
7.48 
17.82 

17.17 
2.20 
6.29 

6.25 
5.23 
11.53 

27.73 
11.68 
9.10 

28.21 
1.99 
2.88 

-0.48 
9.69 
6.72 

21.11 
10.49 
9.43 

12.47 

1.38 
2.26 

16.11 

8.64 
9.11 

__UT 

24.92 

Growing 

Replenishing 

Year.  . 

48.67 

25.66 

23.01 

48.51 

32.58 

15.93 

41.03 

1893. 

1894. 

1895. 

Storage             * 

22.84 
11.01 
7.58 

12.40 
1.90 
2.51 

10.44 
9.11 
5.07 

21.00 
7.79 
10.94 

39.73 

10.25 
1.24 
2.04 

13.63 

10.76 
6.65 
8.90 

20.18 
11.79 
18.66 

11.29 
1.45 
6.17 

8.89 
10.34 
12.49 

Growing  

Replenishing  

Year  . 

41.43 

16.81 

24.62 

26.20 

50.63 

18.91 

31.72 

1896. 

1897. 

18k 

Storage  „.. 

20.91 
7.69 
14.74 

15.96 
1.55 
3.70 

4.95 
6.14 
11.04 

19.87 
12.34 
9.92 

11.05 
2.57 

2.58 

8.82 
9.77 
7.34 

26.61 
12.71 
16.76 

16.15 
245 

4.26 

10.46 
10.26 

12.50 

Growing 

Replenishing  

Year  .  .  . 

43.34 

21.21 

22.13 

42.13 

16.20 

25.93 

56.08 

22.86 

33.22 

1899. 

1900. 

Storage.    .  , 

22.31 
8.16 
10.01 

18.38 
.23 
1.63 

3.93 
7.93 

8.38 

28.30 
9.25 
13.01 

14.09 
1.49 
2.72 

14.21 
7.76 
10.29 

Growing   . 

Replenishing..  . 

Year  _  

40.48 

20.24 

20.24 

50.56 

18.30 

32.26 

Mean    for    5    years, 
1896-1900,  inclusive.  , 

Mean    for    38    years 
1863-1900,  inclusive. 

Storage  

23.60 
10.03 
12.89 

15.  13 

1.66 
2.98 

8.47 
8.37 
9.91 

23.15 
11.59 
12.38 

14.92 
2.08 
3.32 

8.23 
'  9.51 
9.05 

Growing  

Replenishing  

Year  

46.52 

19.77 

20.75 

47.  13 

20.32 

26.81 

Rainfall,  Run-off  and  Evaporation. 


755 


TABLE  LXXXVII—  Neshaminy  Creek,  1884-1899,  inclusive. 

[Catchment  area=139.3  square  miles.] 


1884 

1885. 

1886. 

Period. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run-v, 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Storage  . 

25  77 

25  61 

0  16 

20  13 

17  85 

2  28 

26  61 

21  45 

5  16 

Growing  

13.71 

1.85 

11.86 

10.25 

1.08 

9.17 

12.67 

1.87 

10.80 

Replenishing  

7.05 

.45 

6.60 

11.22 

1.73 

9.49 

7.60 

.66 

6.94 

Year  

46.53 

27.91 

18.62 

41.60 

20.66 

20.94 

46.88 

23.98 

22.90 

1887. 

1888. 

1889. 

Storage  

21.88 

15.92 

5.96 

26.48 

21.17 

5.31 

22.32 

13.44 

8.88 

Growing  

19.26 

4.44 

14.82 

11.83 

1.01 

10.82 

22.42 

10.00 

12.42 

Replenishing  

7.59 

1.03 

6.58 

14.18 

6.02 

8.16 

22.18 

12.37 

9.81 

Year 

48  73 

21  39 

27  34 

52  49 

28  20 

24  29 

66  92 

35  8l 

31  11 

. 

1890. 

1891. 

1892. 

Storage   

22.06 

14.85 

7.21 

23.48 

17.74 

5.74 

22.55 

15.01 

7.54 

Growing.                          

14.28 

2.15 

12.13 

15.90 

2.  53 

13.37 

11.58 

1.31 

10.27 

Replenishing  .  .  . 

10.23 

3.33 

6.93 

8.08 

2.  ay 

5.70 

10.13 

1.94 

8.19 

Year  .  

46.57 

20.33 

26.24 

47.46 

22.65 

24.81 

44.26 

18.86 

26.00 

1893. 

1894. 

1885. 

Storage 

22  16 

18  52 

3  64 

26  68 

18  16 

8  52 

20  97 

15  84 

5'  13 

Growing  

12.21 

1.70 

10.51 

8.95 

1.82 

7.13 

11.41 

2.07 

9.34 

Replenishing     

11.07 

3.74 

7.33 

16.45 

6.12 

10.33 

6.21 

.24 

5.97 

Year  

45.44 

23.98 

21.48 

52.06 

26.10 

25.98 

38.59 

18.15 

20.44 

1896. 

1897. 

Storage  

20.52 

11.54 

8.98 

19.28 

10.60 

8.68 

Growing  

10.80 

1.65 

9.15 

17.70 

6.50 

11.20 

Replenishing 

12  65 

3  41 

9  24 

9  06 

3  11 

6  95 

Year 

43.97 

16.60 

27.37 

46.04 

19.21 

26  83 

1898. 

1899. 

Storage 

25.68 

16.87 

8.81 

33.09 

20.60 

2  59 

Growing 

12.34 

1.69 

10.65 

9.41 

1.76 

7.66 

Replenishing 

12.80 

3.33 

9.47 

10.91 

1  96 

895 

Year  

50.  82 

21.89 

28.93 

43.41 

24.22 

19.19 

756 


Miscellaneous  Tables. 


TABLE  LXXXVIII— Perkiomen   Creek,   1884-1899,   inclusive. 
[Catchment  area=152  square  miles.] 


1884. 

1885. 

1886. 

Period. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Storage 

25.25 

25.19 

0.06 

20.47 

15.29 

5.18 

26.03 

19.74 

6.29 

Growing 

15.53 

4.07 

11.46 

9.83 

1.68 

8.15 

11.76 

3.35 

8.41 

Replenish!  ng 

7.54 

1.59 

5.95 

9.49 

2.3& 

7.11 

9.00 

2.02 

6.98 

Year    

48.32 

30.85 

17.47 

39.79 

19.35 

20.44 

46.79 

25.11 

21.68 

1887. 

1888. 

1889. 

Storage 

21.63 

14.66 

6.97 

27.48 

19.67 

7.81 

22.99 

14.28 

8,71 

Growing               

17.28 

4.26 

13.00 

12.42 

2.17 

10.25 

23.38 

10.02 

13.36 

Replenishing     

6.70 

1.45 

5.25 

14.18 

7.40 

6.78 

20.45 

11.81 

8.64 

Year 

45.59 

20.37 

25.22 

54.08 

29,24 

24.84 

66*82 

36.11 

30.71 

1890. 

1891. 

1892. 

Storage   .. 

24.68 

18.15 

6.53 

22.89 

17.35 

5.54 

23.64 

15.89 

7.75 

Growing 

14  35 

3  11 

11  24 

18  32 

&25 

15  07 

11  06 

2  3a 

8  68 

Replenishing 

10  31 

4  52 

5  79 

8  15 

2  69 

5  46 

9  33 

2  66 

6  67 

Year  

49.34 

25.78 

23.56 

49.36 

23.29 

26.07 

44.03 

20.93 

23.10 

1893. 

1894. 

1896. 

Storage 

22  16 

17  21 

4  95 

24  37 

15  77 

8  60 

23  22 

15  51 

7  71 

Growing 

12  20 

1  82 

10  38 

8  77 

2  05 

6  72 

10  88 

1  32 

9  56 

Replenishing  

10  18 

3  33 

6  85 

15  40 

5  18 

10  22 

6  25 

75 

5  50 

Year 

44  54 

22  36 

22  18 

48  54 

23  00 

25  54 

40  35 

17  58 

22  77 

1896. 

1897. 

Storage  

19  99 

10  26 

9  73 

20  00 

12  37 

7  63 

Growing  

15  05 

2  83 

12  22 

13  69 

3  08 

10  61 

Replenishing    . 

14  62 

4  19 

10  43 

10  07 

2  26 

7  81 

Year  

49  66 

17  28 

32  38 

43  76 

17  71 

26  05 

1898. 

1899. 

Storage  

24  24 

15  74 

8  50 

22  79 

20  49 

2  30 

Growing  

9  98 

1  39 

8  59 

14  12 

2  46 

11  66 

Replenishing  ,. 

13.85 

3  90 

9  95 

11  36 

4  01 

7  35 

Year  ,  

48  07 

•  21  03 

27  04 

48  27 

26  96 

21  31 

Rainfall,  Run-off  and  Evaporation. 


757 


TABLE  LXXXIX—  Tohickon   Creek,   18S4-1898,   inclusive. 
[Catchment  area=102.2  square  miles.] 


1884. 

1885. 

1886. 

Period. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration. 

Rain- 
fall. 

Run- 
off. 

Evapo- 
ration 

Rain- 
fall.' 

Run- 
off. 

Evapo- 
ration. 

Storage  

26.06 

27.27 

-1.21 

21.86 

19.45 

2.41 

28.54 

27.79 

0.75 

Growing  

17.52 

6.53 

10.99 

11.31 

1.54 

0.7? 

11.10 

2.27 

8.83 

Replenishing  

7.97 

1.35 

6.62 

10 

2.94 

7.06 

9.05 

2.04 

7.01 

Year 

51  55 

35  15 

16.40 

43  17 

23  93 

19  24 

48  69 

32  10 

16  59 

1887. 

1888. 

1889. 

Storage  .    .  .  ,  >  

21.60 

18.44 

3.16 

28.52 

27.  i7 

1.15 

25.13 

17.82 

7.31 

Growing  

19."19 

4.80 

14.39 

12.96 

1.99 

10.97 

23.90 

12.45 

11.45 

Replenishing  

6.71 

.91 

5.80 

16.04 

10.14 

5.90 

21.34 

18.70 

7.64 

Year 

47,50 

24.15 

23.35 

57.52 

39.50 

18.02 

70.37 

43  97 

26.40 

1890. 

1891. 

1892. 

Storage 

25.09 

19.01 

6.08 

23.07 

20.23 

2.84 

23  43 

19  76 

3  67 

Growing 

15.49 

2.54 

12.95 

19.77 

4.99 

14.78 

11  22 

1  52 

9  70 

Replenishing 

10.20 

5.45 

4.75 

7.16 

2.03 

5.13 

10  65 

3  47 

7  18 

Year  

50.78 

27 

23.78 

50 

27.25 

22.75 

45.30 

24.75 

20.55 

1893. 

1894. 

1895. 

Storage   ... 

22.82 

22.05 

0,77 

27.04 

21.65 

5.39 

21.35 

19.91 

1  44 

Growing                

14.82 

2.10 

12.72 

6.95 

.84 

6.11 

12.45 

1.46 

10  99 

Replenishing    

11.81 

4.06 

7.25 

17.63 

8.11 

9.52 

6.63 

.28 

6  35 

Year  

48.95 

28.21 

20.74 

51.62 

30.60 

21.02 

40.43 

21.65 

18.78 

1896. 

1897. 

1898. 

Storage 

21.69 

12.30 

9.39 

20.82 

13.93 

6.89 

26.40 

21  30 

5  20 

Growing             

13.76 

2.91 

10.85 

17.32 

5.12 

12.20 

10.87 

1 

9  87 

Replenishing  .  ^  

12.58 

4.52 

8.06 

8.78 

1.98 

6.80 

13.80 

5.19 

8  61 

Year 

48  03 

19  73 

28  30 

46  92 

21  03 

25  89 

51  07 

27  39 

23  68 

\ 


INDEX 


PAGE 

Abbe,   evaporation  relations 141 

Acceleration, 

and  retardation  of  water  in 

penstock    690 

curve  of 689 

effect  of,   on   water  supplied 

to   wheel    455 

of    gravity    06 

Action,     turbines     (see     Impulse 

Turbines)     244 

Adam's,   A.   L.,   Values   of   coeffi- 
cients for  wood  stave  pipe ....     60 

Air   chamber    461 

Air,  energy  in 22 

Allis  Chalmers  Co., 

Sewalls  Falls  turbines 512 

turbine    governor 735 

Turner's  Falls  power  plant..  514 
Altitude,  effect  of  on  rainfall ...  124 
American  turbines.  11, 13,  249,  256,  266 

buckets  of 275 

Fourneyron  250 

Francis 2 48 

impulse    275 

Jonval 252 

practice  of  various  manufac- 
turers in  measuring  the  di- 
ameter of  28G 

reaction,  type,  efficiency  of. .   247 
catalogue  relations  of  diam- 
eter and  speed  of 326 

relations     of     diameter     and 

discharge  of  339 

relation  of  power  and  diam- 
eter of 342 

relation  of  speed  and  dis- 
charge in 346 


!  American  Turbines — Con.  PAGE 

relation  of  speed  and  power 

in 350 

specific  speed  of  350 

Ampere     33 

Aprons     for     dams,     preliminary 

study  of,  for  dam  at  Kilbourn. .   585 
Archibald,    E.    M.,    discussion    of 
effect  of  load  factor  on  cost  of 

power    622 

Atkins'  wheel  and  case 273 

Atlantic  drainage,  hydrographs. .   190 
Auxiliary  power, 

cost  of    65S 

effects  of 631 

hydrograph  showing  amount 
of,   necessary   to   maintain 

power  at  Sterling,  111 635 

necessary   to   maintain   fixed 

power  on  a  southern  river  633 
study  of,  for  report  on  water 
power    680 

B. 

Back  water  curve 58 

literature  on 78 

study  of,  for  report  on  water 

power    678 

Barker's  mill 5,  239 

Bazin's  formula 50,  69 

diagram   for   solution   of. ...     51 
Bearings, 

Geylin    glass    suspension 290 

horizontal  lignum  vitae 295 

hydraulic  balancing  piston  of 
Niagara    Falls    Power    Co. 

293, 294 
of  horizontal  turbines 292 


760 


Index. 


Bearings — Con.  PAGE 

vertical     cross     or     hanging 
bearings   of  Niagara  Falls 

Power   Co 293 

vertical  turbine 289 

Belt    losses 30 

Bends  in  a  stream,  effect  of  on 

distribution   of  velocity 212 

Betiva     Dam,     India,     automatic 

drop  shutter  for 610 

Bmn<ie,   Alexander  A 125 

Borda    turbine 241 

Boyden,  Uriah  A 9 

diffuser  305, 307 

Fourneyron  turbine  of. .  249,  251 

turbine  of 250 

turbine  tests  of 360 

Brake  wheel,  W.  O.  Weber 376 

Breast  water  wheels 3 

British    thermal    unit 32 

equivalents  of 34 

per  minute,  equivalents  of . .     35 

Brown,   Ralph   T 275 

Buckets, 

American     276 

Dodd's     274 

Ellipsoidal     274 

Hug's    274 

Knight's  274 

Moore's  274 

Pelton  274 

modern  changes   in 13 

of     tangential      or      impulse 
water  wheels 274 

C. 

Cadiat's    turbine 239 

Canals, 

determination     of     economic 

cross  section 54 

of     Holyoke     Water     Power 

Company    568 

for   Peshtigo   River    develop- 
ment       573 

Capacity, 

influence  of  choice  of  machin- 
ery on 525 

of  each  part  of  a  system...     25 
of  prime  movers'. .  .   528 


Capacity — Con.  PAGE 

Case       Turbine       Manufacturing 

Company, 
tests  of  a  30"  regular  turbine  725 

tests  of  a  30"  special 724 

Channel    condition,    effect    of    on 

gradient  203 

Channel  grade,  effects  of  on  the 

hydraulic  gradient  of  a  stream  204 
Characteristic  curve, 

consideration,    of    a    turbine 

from    401 

of    Tremont-F  ourneyron 

wheel    409 

of  a  45"  Samson  wheel..   410-411 
of  a  turbine,  construction  of  400 

of  a  Victor  turbine 402-403 

of  Improved    New    American 

turbine   406 

of       Wellman-Seaver-Morgan 

51"  turbine 408 

Chase,     Mr.     Stewart,     agent     of 

Holyoke  Water   Power  Co 361 

Chestnut  Hill  reservoir,  evapora- 
tion from  water  surface  of...  143 

Chesuncock  log  way 620 

Chezy's    formula 46 

applied  to  pipes 60 

diagram  for  the  solution  of  52-53 

Chinese  Nora 1 

Chippewa  River . , 165 

Christiana  Power  Station,  Nor- 
way, typical  electrical  lighting 

load  curve 424 

Chute  case,  the 297 

Closed  penstock,  predetermina- 
tion of  speed  regulation  with 

462,464 

Cochituate  basin,  relations  be- 
tween precipitation,  evapora- 
tion, run-off  and  temperature 

on     149-150 

Coefficients, 

of  discharge  for  weirs 65,74 

of     discharge     through     sub- 
merged  orifices   and    tubes     45 

of  entrance    losses 42 

relation   of   to    hydraulic    ra- 
dius on  Wisconsin  River..   199 


Index. 


761 


PAGE 

Columbus  Power  Company,  plant  546 
Combes,  tests  of  reaction  wheels  359 

Compound  motion 37 

Conant,  R.  W.,  estimate  of  operat- 
ing   expenses    of   various    rail- 
way   power    stations 660 

Concord  Electric  Company,  plant 

of   55?, 

Connecticut  River,  table  showing 
relation  of  rainfall  to  run-off 
on  the  storage,  growing  and  re- 
plenishing period 159 

Connections  of, 

governor  to  gates 493 

by  cable  477,  495 

by  draw  rods 492 

by  shafts  and  sectors...   494 
turbines  to  machinery,  vari- 

ious   methods ' 531 

vertical  wheels  to  generator  507 
Connorsville,  Indiana,  regulation 

of  pumping  plant 441 

Conservation,  laws  of  energy 21 

Constantine,  Michigan, 

details  of  head  gates  at 613 

elevation  of  head  gates  at. .   613 
rear  view  of  head  gates  at. .   613 

Contractions   42 

Control  of  governor  from  switch- 
board    492 

Conversion  of, 

energy  units 33 

power    26 

Cornell  Hydraulic  Laboratory, 
experiments  on  float  measure- 
ments by  Kuichling,  Williams, 

Murphy  and  Boright 229 

Cost, 

effect  of  size  of  units  on ....   526 

of  auxiliary  power 658 

of  coal,  effect  of  on  the  cost 

of    power 665 

of  developed  water  power...   652 
of  development     of     various 
American      water      power 

plants 650 

of  development     of     various 
foreign  water  power  plants  651 


Cost — Con.  PAGE 

of  development       of       water 

power    647 

of  distribution  of  power 653 

of  gas  power,  estimate  of . . .   685 

of  motor  installation 657 

of  operation,  estimate  of  for 
various  proposed  Canadian 

plants   654 

of  operation  of  various  street 

railway   power   stations. . .   661 
of  water  power  development, 
relation  of  capacity  to ....   648 

relation  of  head  to 649 

of   water   power    plant,    esti- 
mate of  Canadian 649 

Cost  of  power, 

effect  of  cost  of  coal  on....   665 
effect  of  partial  load  on....   654 

from   sub-station 656 

literature    on 672-673 

per  H.  P.  per  annum  in,  vari- 
ous plants 659 

transmission  656 

steam  at  22  power  plants. . . .   660 

steam,  estimate  of 664 

steam       generated       electric 
power  to  the  consumer...   669 

water  power 647 

Cost,  value  and  sale  of  power...   646 

Coulomb     33 

Crest,  effect  of  changes  in  lengths 

on   head 100 

Crops,  daily  consumption  of  water 

by    135 

Cross  section,  and  slope,  estima- 
tion of  flow  from 219 

Croton  River,  rainfall,  run-off  and 

evaporation  751 

Cubic  foot,  equivalents  of 34 

Current  meter, 

methods  of   computation   for  227 
observations  and  computation  223 

Price's    electric 222 

rating  curve 224 

rating  station  at  Denver,  Col- 
orado    223 

readings,  method  of  making  225 
the    use    of . .  .   221 


762 


Index. 


PAGE 

Current   wheels 1,  241 

Cylinder  gates 299-300 

diagram       showing       eddies 
caused    by 302 

D. 

Dam  and  power  plant,  relations 

of 561 

Dam  at, 

Holyoke   during  flood 591 

Danville,   Illinois,   section  of  592 
Kilbourn,     Wisconsin,     with 

movable    crest 60S 

McCall's   Ferry,   section   of. .   592 

Sewell's   Falls,    timber 594 

of     Holyoke     Water     Power 

Company    590 

of  The  Montana  Power  Com- 
pany, near  Butte 593 

Dams, 

appendages    to 603 

aprons  for 585 

calculations    for    stability    of  587 
consideration  of  various  fac- 
tors   in 589 

effect  of  design  of,  on  head  100 

flood   flows    over 583 

for  water  power  purposes. . .   579 

foundations  of 581. 

heights  of 580 

impervious  construction  of. .   586 

literature    on 595 

movable    100, 603 

object  of  construction  of. ...  579 

overturning  of 586 

plants  -located   in 574 

preliminary     study    of    dam 
for      Southern      Wisconsin 

Power  Co 585 

principles  of  construction  of 

579-581 

sliding  on  base 586 

stability  of  masonry 586 

timber     crib     at     Janesville, 

Wis 582 

types  and  details 594 

Danaide    turbine..  .   241 


PAGE 
Danville,    Illinois,    concrete    and 

timber    fishway   at 619 

Danville,  Illinois,  section  of  con- 
crete dam  at 592 

Dayton   Globe   Iron  Works  Com- 
pany      256 

American     turbine,     develop- 
ment  of 258 

increase  in  speed  of....   259 

runner    of 260 

characteristic     curve    of     an 
Improved    New    American 

turbine    406 

double  horizontal  wheel 515 

double    horizontal    wheel    in 

closed  penstock 516 

test  of  a  44"  turbine 714 

two  pairs  of  turbine  units  in 

tandem 518 

Deflecting  nozzle,   governing   im- 
pulse wheel  with 470 

Denver,  Colorado,  current  meter 

rating    station ~ 223 

Depreciation 652 

literature  on 674 

Developed  power,  annual  cost  of  562 
Development  of, 

American  turbine 25S 

capacity,  speed  and  power  of 

a  48"  turbine 257 

Leffel's    wheel 260 

potential   energy 19 

the  turbine 4 

water  power  in  the  U.  S. . . .     14 
Diameter, 

graphical  relations  of  dis- 
charge to 338 

of    runner 285 

of  a   turbine,   expression   for 

relations    of   power    to....   338 
of  a  turbine,  relation  of  dis- 
charge to 337 

of  turbine  water  wheels,  prac- 
tice of  various  manufac- 
turers in  measuring 286 

Diameter  and  discharge  of  vari- 
ous American  turbines..  .   339 


Index. 


763 


PAGE 

Diameter  and  power, 

graphical  relation  of  in  tur- 
bines of  homogeneous  de- 
sign    341 

of  various  American  tur- 
bines    342 

Diffuser,  Boyden 305-307 

Discharge   and   speed   of  various 

American   turbines. 346 

Discharge    curve 95 

of   Potomac    River 232 

Discharge,  curves  of  at  various 
gate  openings  under  given 
speed,  calculated  from 
actual  tests 398 

graphical  relations  of  dia- 
meter to 338 

measurement  of 372 

of  a  turbine  at  a  fixed  "gate 
opening  332 

of  certain  American  and 
European  rivers,  rates  of 
maximum  flood 168 

of  rivers,  relation  to  rainfall  745 

of  thirteen  water  wheels  of 
homogeneous  design  and 
different  diameters 337 

of  turbine  proportional  to 
square  root  of  head 332 

of  turbines,  relation  of  speed 
to  345 

of  various  Michigan  rivers..   188 

of  various  turbines  at  full 
gate,  graphically  ex- 
pressed    333 

of  wheel  under  fixed  gate  con- 
ditions, equation  for 332 

over  weirs,  comparative ....  68-69 

relation  of  diameter  to,  in 
American  turbines 339 

relation  of  power  to  diameter 
of  a  turbine 337 

relations  of  speed  to  for  a 
12  inch  Smith-McCormick 

turbine    335 

Distribution  of, 

power,    cost    of 653 

rainfall .   ill 


Distribution  of — Con.  PAGE 
total  annual  rainfall  in  Wis- 
consin        114-115 

velocity,  effects  of  ice  cover- 
ing        215 

water  at  various  plants,   ex- 
amples   of 567 

weekly  rainfall  in  Wisconsin  117 
Dix,  J,  L.  &  S.  B.,  Jonval  turbine  255 

Doble,  ellipsoidal  bucket 274 

needle    nozzle 302-306 

nozzle,    stream    from 307 

runner    277 

tangential   wheel    248 

Dodd   bucket    274 

Dodge  Manufacturing  Co.,  instal- 
lation   by 533-534 

Dolgeville     Electric     Light     and 

Power  Co.,  plant  of 548 

Draft   Tube,   the 302-304 

Drainage  area,  relations  to  flood 

discharge   168 

Drop-shutter,        automatic        for 

dam  610 

Duration  curves  of: 

Ausable   River 187 

Grand  River   at   Grand    Rap- 
ids       187 

Grand  River  at  North  Lans- 
ing        187 

Kalamazoo    River 187 

St.  Joseph  River 187 

Thunder    Bay   River 187 

various   Michigan   rivers   for 

1904     187 

Dynamo,  efficiency    of 24 

E. 

Earthen  dams,  literature  on 596 

Eastern     Gulf    drainage,     hydro- 
graphs    of 190 

Eau      Claire,      adjustable      flash- 
boards  at 61 L 

Economy, 

principles    of 32 

value    of    improvements    in- 
tended to    effect 670 

Economy   in   operation   of  power 
Plant   .527 


764 


Index. 


PAGE 

Economy  Light  and  Power  Co., 

Joliet  plant  of 571 

Morris   plan,t   of 572 

tainter  gates  for  Morris  plant  605 
wheels    of 410-411 

Eddies, 

as  caused  by  cylinder  gate..   302 
as  caused  by  partial  closure 

of  register  gates 305 

through     opening     and     par- 
tially closed  wicket  gate..   304 

Efficiency     21, 375 

definition  of 23 

natural  limit  to 21 

of  a  combined  plant 24 

of  a  dynamo 24 

of  turbines,   relative 246 

of  a  Fourneyron  turbine....   247 

of  a  furnace 22 

of  American  type  of  reaction 

turbine  247 

of  an  hydro-electric  plant...     24 

of    a    shaft 24 

of  a  steam  engine 24 

of  canal   section 54 

of  Jonval  turbine 247 

of   pumping   engine.... 23 

of   tangential    turbines 247 

of  the  machine 23 

practical  limits  to 23 

relations  of  q>  and 329 

Electric  lighting  load  curve 424 

Electric    lighting,    losses    in    hy- 
draulic plant  for 25 

Electric    units 32 

Emerson,  James, 

testing  of  turbines  by 361 

tests     by 364 

Energy    23 

conservation,  laws  of 21 

definition   of 19 

differentiation    of 20 

equivalent  units  of 740 

exertion  of  by, 

momentum    41 

weight    ; 41 

pressure   41 

in  the  air. .  22 


Energy — Con.  PAGE 

literature  of 39 

losses  in  an  hydraulic  plant  25 
losses  in  a  pumping  plant..  25 
losses  in  steam  power  plant.  24 
mathematical  expression  of  40 

no  waste  of  in  nature 20 

of    fuel 19 

potential   and   kinetic 3'J 

potential 20 

thermal    20 

required  to  change  penstock 

velocity     446, 456 

transmission  and  transforma- 
tion   of 23 

units,   conversion    of 33 

units   of 32 

Enlargements,     sudden 42 

Entrance  head 42 

Equivalent  measures  and  weights 

of    water 740 

Equivalents  of  energy 740 

Escher,  Wyss  and  Company:....   280 
double    turbines    at    Chivres 

near  Geneva 282 

Jonval     turbine     at     Geneva 

Water     Works 281 

Estimate    of  cost,    for    report   on 

water  power 682 

European  practice  in, 

turbine    construction 280 

water    wheel    design 278 

European  type  of  turbine 249 

European   vertical  turbine,   steps 

of   290 

Evaporation,     137 

and    temperature     on     Lake 

Cochituate,    relations    of.  .   150 
annual  in  the  United  States 

138-139 

from  water  surface  in  inches, 
Chestnut  Hill   reservoir...  143 

literature    on 144 

monthly  from  free  water  sur- 
faces, 

Augusta,  Ga.,  Cincinnati, 
Ohio,  Des  Moines,  Iowa, 
Detroit,  Mich.,  Helena, 
Mont.,  Little  Rock,  Ark., 


Index. 


765 


Evaporation— Con.  PAGE 

monthly  from  free  water  sur- 
faces—Con. 

Montgomery,  Ala.,  New 
Haven,  Conn.,  Olympia, 
Wash.,  Palestine,  Texas, 
Sacramento,  Cal.,  Spo- 
kane, Wash.,  Topeka, 
Kans.,  Winnemucca,  Nev., 
Yuma,  Ariz.,  and  at  vari- 
ious  points  in  the  U.  S.. .  140 

of  water 20 

precipitation,       run-off      and 
temperature,     relations     of 
on  upper  Hudson,  River...  154 
rainfall  and  run-off  for  vari- 
ous   periods 750 

relation  to  precipitation,  run- 
off    and     temperature,     on 

Lake   Cochituate 149 

tables    ...  .732 


F. 


Factory   friction   tests,   data  an^d 

results    of 655 

Factory    load   curves 424,  42S 

Faesch    and    Picard 252 

Failures  of  Dams,  literature  on. .   601 

Fairbairn     3 

Fairmont  pumping  station 252 

Falling  stream,  effects  of  on  gra- 
dient      201 

Fanning,  J.  T 15 

Financial  considerations  of  water 

power    development 646 

Fishways :      614 

in  dam  at  Danville,  Illinois,..   618 
in    timber    dam    at    Sterling, 

111 619 

of  Fish  Commission  State  of 

Wisconsin     619 

literature    on 632 

Fitzgerald,    Desmond.     On    evap- 
oration       137 

Fitz      Water     Wheel      Company. 

overshot  water  wheels  of 243 

Five-halves  powers  of  numbers..   744 
Flash  boards,  100,  609 


Flash  Boards — Con.  PAGE 

adjustable    at    Eau    Claire, 

Wis 611 

and   supports,  Rockford  Wa- 
ter Power  Company 609 

literature    on 622 

Float    Measurements 226 

at  Lowell  by  Francis 229 

Float    Wheels, 1-3 

London  water  works 1 

Flood    discharge,    American    and 

European    rivers 168 

of  rivers,  relation  to  rainfall  745 
Flood  Flow,  study  of  for  report 

on  water  power 678 

Flood  flows,  data  on 583 

Flood  gates 606 

Flood  over  Holyoke  dam 592 

Flow, 

comparative    mean    monthly 
of     Wisconsin     and     Rock 

Rivers    178 

distribution   of  velocity   dur- 
ing various  conditions  of. .   212 

effects  of  low  water 107 

estimates  of, 

from  cross  sections   and 

slope    219 

by  weirs 219 

in     open    channels,    methods 

for  the  estimate  of 219 

in   open;  channels,   literature 

of     198 

in    reaction    wheels 317-320 

in  tangential  wheels 316 

measurements  of  by  the  de- 
termination  of   velocity . . .   221 
mean     monthly     of     various 
Eastern  streams,  in  chron- 
ological   order 172 

mean     monthly     of     various 
streams,  arranged  in  order 

of    magnitude 173 

of  water  in  pipes 59 

of  water  through  orifices. ...     64 

over    weirs 64 

power  of  a  stream  as  affected 

by      79 

relations  of  guage  height  to  208 


766 


Index. 


PAGE 

Flow  and  head,  relations  of 83 

Fly-ball    governor, — first    used . .       3 

Fly   wheel 457 

Foot     pound 32 

Foot,     cubic     foot     per     minute, 

equivalents    of 36 

Foot,     cubic     foot     per     second, 

equivalents    of 35 

Foot  gallon,  equivalents  of 34 

Foot  pound,  equivalents  of. ...         34 
Foot  pounds  per  minute,  equiva- 
lents   of 35 

Forests,  effect  on,  evaporation ....   136 
Foster,    H.    A.,    tests     of     steam 

power    plant 660 

Foundations  of  dams... 581 

Fourneyron  turbine,    11,  239,  250,  305 

characteristic  curve  of 409 

data    of 706 

diagram    of    double    turbine 
of  the  Niagara  Falls  Water 

Power    Company 253 

efficiency    of 247 

Fox  River,  hydrograph  at  Rapid 

Croche    628 

Francis,   J.   B 11, 378 

float   measurements   at   Low- 
ell       229 

formula  for  dam  on  the  Mer- 

rimac  River 69 

inward  flow  wheel 256 

tests   by 359 

turbine   at   Boott   Mills,   test 

data    of 703 

turbine,  original 12 

Fraser     River,  high     water     dis- 
charge   at   Mission    Bridge 170 

Friction    loss 44 

in  asphalt  coated  pipe 02 

in  lap-riveted  pipe 63 

in  wood  stave  pipe 63 

Friction    in   pipes,   conduits   and 

channels,  first  principles 44 

Friction  loads  in  factories 655 

Friction      of      reaction      wheels, 

losses  by ' 315 

Frizell's  formula  for  sharp  cres- 
ted   weirs 


PAGE 

Fuel,    energy    of 19 

Furnace    efficiency 22 

G. 

Ganguillet  and  Kutter's  formula     47 
Garratt,  A.  C.,  discussion  of  connec- 
tion of  governors  to  gates....   493 
Gas    plant,    estimate    of    capital 

cost  and  annual  cost 665 

Gate  hoists  and  head  gates. .   611,  617 
Gate  movement,  permissible  rate 

of  451 

Gate    opening,    discharge    of    a    tur- 
bine at  various 332 

Gates  and  guides  of  Girard  Im- 
pulse turbine 306 

Gates, 

cylinder    300 

details  and  operating  devices 
of  Snoqualmie  Falls  tur- 
bine    303 

flood    606 

for     overshot      and      breast 

wheels      3 

register    301 

wicket     300-301 

Guage  heights, 

and   heads   available   at   Kil- 

bourn,    Wis 99 

fluctuations  in 200 

relations  at  various  stations 
on  the  Wisconsin  river. . . .  206 

relation  of  to  flow 208 

Gears  and  shafting,  losses  in. ...     2i) 
Generators  and  motors,  ordinary 

efficiency    of 31 

Generation    and    transmission    of 

energy,  power  losses  in 27 

Generation  of  power  from  poten- 
tial source 26 

Genesee  River,  run-off  diagram..   155 

Geneva,  Switzerland, 280 

water  works,  Jonval  turbine 

at   281 

Geological  conditions, 

effects  on  run-off 177 

study  of  for  report  on  water 
power  .  .  677 


Index. 


767 


PAGE 

Geylin  Glass  suspension   bearing  290 

Geylin-Jonval  turbine 

249,  254,  290,  299 

of  Niagara  Falls  Paper  Mill 

Company    256 

Girard  turbines, 

current  239 

Gates  and  guides  of 306 

general  view  of 280 

impulse    278 

longitudinal  section  of..   279 

runners    of 284 

with  draft  tube 278 

runner    of 280 

Girard  type   for   partial   tur- 
bine       273 

type  of  water  wheels 

269,    276,    307 

Glocker-White    turbine    governor  735 
Governing, 

impulse  wheels  with  deflect- 
ing  nozzles 470 

regulation       with       variable 

speed  and  resistance 441 

water  wheels,  present  status 

of   443 

Governor, 

Allis  Chalmers  hydraulic 735 

anti-racing   mechanical 473 

calculations,        nomenclature 

for    447 

connections, 

by  cable 477,   495 

by    draw    rods 492 

by  shaft  and  sectors. . . .  494 
control  from  switchboard. . . .  492 
details  and  application  of 

Woodward   477 

diagram  of  Lombard-Replogle 

mechanical    479 

effect    of     sensitiveness     and 

rapidity    of 457 

essential   features   of  an   hy- 
draulic      481 

for  water  wheels  first  used  3 
general  consideration  of....  491 
Glocker-White  .  .  735 


Governor — Con.  PAGE 
Lombard-Replogle       mechan- 
ical       478 

Lombard  type  "N"  hydraulic  480 
operating  results  with  Lom- 
bard       485 

problem  of  water  wheel 445 

section    and   plans   of   Wood- 
ward     476 

section  of  Woodward  vertical 
compensating      mechanical  475 

simple  mechanical 472 

Sturgess    hydraulic 486 

the    ideal 443 

Woodward    compensating. . . .   474 

Woodward    standard 471 

specifications    467 

Grade,  effect  of  change  in 205 

Gradient,    effect   of   channel    con- 
ditions  on 203 

effects    of    rising    or    falling 

stream   on 201 

Granid    River,    at    Lansing    Mich- 
igan     165 

Graphical, 

analysis  of  relation  of  power, 
head  and  flow  at  Kilbourn, 

Wisconsin    105 

determination  of  stream  flow 

from     measurements 230 

investigation     of     the     rela- 
tions of  power  to  head  and 

and    flow 103 

relation  of  energy  and  veloc- 
ity in  reaction  turbines...   321 

representation  of  head 97 

representation  of  the  laws  of 

motion    38 

study    of     head 104 

study  of   power  at  Kilbourn  104 

Gravity   wheels 237,    233 

Great  Lakes,  hydrograph  of  dis- 
charge of  the 180 

Growing  period 157 

Guides  and   buckets   of  Tremont 

turbine     251 

Gulf  drainage,  hydrographs  of.. 

190,    192 


768 


Index. 


H. 

PAGE 

Hand  of  water  wheels 289 

Hanging    bearing,     the    Niagara 

Falls   Power   Company 293 

Harness  and  driving  sheaves, 
Southwestern  Missouri  Light 

Co 533 

Harper,   John   L.,  tests  of  Leffel 

turbines  at  Niagara 380 

Harrington,  N.  W.,  effect  of  for- 
ests on  rainfall  and  evapora- 
tion    133 

Hartford  Electric  Light  Co., 

increase    in    sale    of    energy 

of   423 

load  curve  of 422 

Head,  at  Kilbourn   dam 581 

showing    changes    in....     99 
under  various  conditions     97 
effect  of   design   of   dam   on 

available    100 

entrance     42 

friction     44 

graphical  representation  of . .     97 

graphical  study  of 104 

measurements  of 373 

on  turbines,  relation  to  speed 

and    diameter 324 

study  of  for  report  on  water 

power    67S 

variations    in 93 

velocity    41 

velocity   in    feet   per   second 

due    to 741 

Head  and  flow, 

importance  of  for  power  pur- 
poses          79 

relations    of 83 

variations    of 83 

Head  and  power, 

effect   of  number   of   wheels 

on    108 

selection  of  turbine  for  uni- 
form      38? 

Head  gates, 

at  Constantine,  Michigan  612,  613 
details  of  for  Mr.  Wait  Tal- 
cott,  Rockford,  Illinois..    .   616 


Head  Gates — Con.  PAGE 

rear  view  of,  at  Constantine, 

Michigan    613 

Head  race,  plants  with 570 

Head  water   curve 96 

Heat, 

solar,     20 

units    of, 32 

Heights  of  dams,  limit  of 580 

Henry,  Professor,  conclusions  on 
the  reliability  of  rainfall  rec- 
ords    125 

Henschel    turbine 233 

Hercules  turbine,  test  of  a  54  inch  710 

High  head  developments 575 

High  head  or  type  "B"  runner..   268 
High  water,  Fraser  River  at  Mis- 
sion, Bridge,   B.  C 170 

History  of  water  power  develop- 
ment   1, 14, 16 

Hoist  for  tainter  gates 606 

Holyoke  Machine   Company,   test 

of  a  54  inch  turbine 710 

Holyoke  testing  flume, 364,  370 

arranged   for  horizontal   tur- 
bines      367 

plan  of 366 

Holyoke  Water  Power  Company, 

canals  of 568 

view  of  dam  during  flood.  . . .   591 
view  of  masonry  dam  of....   590 

Horse   power, 32 

and  efficiency  of  proposed  tur- 
bines    for     McCall     Ferry 

Power    Company 418 

equivalents    of 34 

speed  relation  of  from  tests  415 

Horse  power  hour 33 

Houck  Falls  power  station,  test 
of  Victor  high  pressure  turbine 

at   382 

Howd-Francis    turbine 249 

Howd,  Sanruel  B 11 

wheel    of 256 

Hudson  River, 

discharge  arranged  in  chrono- 

ical    order 172 

arranged     in     order     of 
magnitude   174 


Index. 


769 


Hudson  River — Con.  PAGE 

run-off  diagram  of 155 

table  showing  relation  of 
rainfall  to  runoff  for  the 
storage,  growing  and  re- 
plenishing period 158 

Hudson    River    Power    Transmis- 
sion Company, 
speed  records  from  plant  of       48G 

Spier's  Falls  plant  of 546 

Hug    bucket 274 

Hunking,  A.  W.,  notes  on  water 

power    equipment 338 

Hunting     or     racing     of     water 

wheels    447 

Hunt-McCormick    runner 267 

Hunt  runner  of  The  Rodney  Hunt 

Machine    Company 269 

Hurdy-Gurdy   wheel 241 

Hydraulics,  general  literature  on     75 
Hydraulic  governor, 

Allis    Chalmers 735 

details   of  Lombard 481 

essential   features  of 481 

Glocker-White    735 

Sturgess  type   "N" 488 

Sturgess,    the 486 

Hydraulic  gradient, 

effects  of  channel  grade  and 

obstructions    on 204 

effects  of  variable  flow  on...   200 
of  a  stream, 

after  construction  of  dam  94 
effects  of  variable  flow  on  202 
under  various  conditions 

of   flow 93 

Hydraulic     plant,    energy    losses 

in  25 

Hydraulics,     40 

of  the  turbine... 309 

Hydraulic  type  of  relay 471 

Hydro-electric  plant, 

efficiency    of 24 

losses    in 26 

Hydrographs,    80 

as  power  curves 89 

available  at  some  other  point 

on  the  river 82 

available  on  other  rivers 83 

47 


Hydrographs — Con.  PAGE 

comparative    from     different 
hydrological    divisions    of 

the  U.  S 184,  189 

continuous  24  hour  theoreti- 
cal power  at  Kilbourn ....     88 
for  full   range  of  conditions 
of  rainfall  and  temperature     82 

when  none  are  available 85 

of, 

Alcovy   River 191 

Atlantic      and      Eastern 

Gulf   Drainage 190 

Ausable   River 186 

Bear  River,  Utah 193 

Chittenango   River 191 

Clear    Creek 192 

Coosa   River 190 

Discharge  of  Great  Lakes  180 

Fox  River 628 

Grand  River 

at   Grand    Rapids... 

186, 191 
at    North    Lansing..   186 

Hood    River 193 

Iron  River,  Michigan...   191 

Kalamazoo    River 186 

Kalawa  River 193 

Kennebec    River 19$ 

Kern  River 193 

Licking    River 190 

Meramec   River 192 

Mississippi     Valley     and 

Gulf  Drainage 191 

Niobrara   River 192 

Ohio  Valley  and  St.  Law- 
rence   Drainage 191 

Otter    Creek 192 

Passaic    River 1^82-183 

Perkiomen    Creek 190 

Rio   Grande   River 192 

Salt  River 192 

San  Gabriel  River 193 

Seneca   River 190 

Spokane    River 193 

St.    Joseph    River 186 

Tennessee    River 191 

Thunder  Bay  River 186 

Walker  River,  California  193 


770 


Index. 


Hydrographs — Con.  PAGE 

Western  drainage 193 

Wisconsin  River, 

at    Kilbourn,     based 
on      measurements 

at  Necedah 86 

at  Necedah,   Wis.  81,192 

Yadkin    River 190 

Yellowstone    River 192 

power  hydrographs  at, 

Kilbourn    90-91 

Sterling,  Illinois 623 

reliability  of  comparative. ..     87 
showing     continuous     power 
at    Kilbourn,    with    actual 

head    101 

showing   power   of    plant   as 
influenced  by  variable  head  110 

study  of  a  stream  from 181 

use  of  comparative 83 

use  of  local 83 

when  none  are  available 87 

when    available 82 

Hydrological  divisions  of  the  U. 
S.,  comparative  hydro- 
graphs  from 189 

I. 

Ice  conditions, 

maximum  velocities  in  a  ver- 
tical   plane 217 

rating    curve    for... 217 

with     overshot     and     breast 

wheels 3 

Ice  covering,  effects  of,  on  distri- 
bution of  velocity 215 

Illinois  River  basin,  comparison 
of  mean  monthly  rainfall 

and   run-off 147 

Improved  New  American  tur- 
bine    257,  259,  300 

calculations   from    character- 
istic   curves    of 407 

characteristic  curve  of 406 

sectional   plan   of 262 

Impulse  and  reaction  turbines..   311 

relative    advantage    of 245 

conditions  of  operations  of. .   215 


PAGE 

Impulse  turbines    (see  also  Tan- 
gential   Wheels) 

237,241,244,246,301,313 

angle  of  discharge 310 

early  development  of 261) 

efficiency    of 247 

governing  of 470 

regulation    of 452 

J. 

James  Leffel   and   Company 266 

characteristic  curve   of  a  45 

inch  Samson  wheel...   410-411 
curve       showing       efficiency, 
power    and    discharge,    un- 
der   various    heads,    calcu- 
lated    from     characteristic 

curves 412 

double  horizontal  turbine. . . .   517 
double      horizontal      turbine 

manufactured    by 265 

double   runner   of 26'i 

four  pairs  of  45  inch  Samson 

horizontal    turbines 523 

tests  of  wheel  at  Niagara. . . .   380 
Janesville,  Wisconsin : 

dam  during  high  water 583 

dam  during  moderate  flow..   583 

dam  showing  low  water 582 

Joliet    plant    of    Economy    Light 

and  Power  Company 571 

Joliet,  water  power  at 22 

Jolly,  J.  &  W.,  Holyoke,  Mass.,..   248 
test  of  a  57  inch  turbine. . . .   70S 

test  of  a  51  inch  turbine 711 

Jonval,    8 

turbine,    239-255 

efficiency    of 247 

at  the  Geneva  Water  Works  281 

tests  of  a  30  inch 725 

tests  of  a  30  inch  special 724 

the     American . .   252 

K. 

Kennebec  River  discharge, 

arranged  in  order  of  magni- 
tude        17.! 

chronologically     arranged...   172 


Index. 


771 


Kilbourn  dam, 

diagram  showing  changes  in 

head    at 99 

head     under    various     condi- 
tions of  flow 97 

Kilbourn,    Wisconsin: 

guage      heights      and      head 

available    at 99 

graphical  study  of  power  at  104 

head  gate  hoists  at 617 

hydrograph  showing  continu- 
ous power  with  actual  head  101 
hydrograph  showing  24  hour 

horse  power 88 

hydrograph  of  Wisconsin 
River  based  on  flow  at  Ne- 

cedah,    Wis 86 

plant  of  Southern  Wisconsin 

Power    Company 521,    569 

power    hydrograph 90 

power      hydrograph,      H.     P. 

hours  with  pondage 10, 19 

power    of   the   wheels    under 

variations   in   flow 106 

rainfall    above 129 

Kilowatt   hour 33 

Kinetic  energy 33,   34,   36 

Knight  bucket 274 

Koechlin    8 

Kuichling,  Emil: 

discussion     of     rainfall     and 

run-off    162 

graphical  relations  of  dis 
charge  area  for  maximum 
flood,  American  and  Euro- 
pean rivers 168 

Kutter's    coefficient    "n" 47 

Kutter's  formula 47 

diagrams  for  the  solution  of  48-49 

L. 

Lake  Cochituate,  rainfall,  run-off 

and    evaporation 763 

Lake    Superior    Power   Company, 

pJant    of 570 

Lap-riveied    pipe,    friction    losses     63 
Laws:   of  energy  conservation...     21 
of    motion,    graphical    repre- 
sentation   of . .  38 


Laws — Con.  PAGE 

of  motion,   Newton's 36 

Laxy  overshot  water  wheels  (see 

frontispiece)    14 

Leffel    and   Company,  the   James 
(See   also   James   Leffel   & 

Co) 13 

tests  of  a  56  inch  turbine...  709 
test  of  a  45  inch  Samson  tur- 
bine     713 

Leffel   turbine, 249 

diagram     of     efficiency,     dis- 
charge and  power  at  Niagara  380 

tests  of,  at  Logan,  Utah 379 

Lighting,  losses  in  generation  and 
transmission  of  power  for....     30 

Limit  turbines. 244 

Lippincott,  J.  B.  and  S.  G.  Ben- 
nett,   relations    of    rainfall    to 

run-off  in  California 177 

Literature: 

back  water  and  interference     78 

causes   of    rainfall 131 

concerning  dams 595 

descriptive  of  hydraulic  and 

hydro-ejectric    plants 556 

disposal  of  rainfall 144 

effect  of  altitude  on  rainfall  132 

evaporation   144 

floods    190 

flow  of  water  over  weirs. ...     77 
flow  of  water  through  pipes     76 

general     hydraulic. 75 

measurement  of   rainfall 132 

power  and  energy 39 

percolation    144- 

relations     of     rainfall     and 

stream  flow    195 

results  of  stream  flow  meas- 
urements      194 

stream  gauging   233 

turbines     353 

turbine    testing 383 

water    power    development . .     16 
Lloyd,  E.  W.,  data  concerning  the 
power  load  on  various  central 
stations,  due  to  various  classes 
of   consumers .   667 


772 


Index. 


PAGE 

Load  conditions  for  maximum  re- 
turns    431 

Load  curve 420 

factory    424 

for  sharp  thunder  storm  peak  426 
in  relation  to  machine  selec- 
tion      433 

New  York  Edison  Company, 

for  day  of  maximum  load. .   425 
of    Hartford    Electric    Light 

Company    422 

of  light  and  power  plant 421 

literature    on 439 

maximum  days  of  pumping, 

London  Hydraulic  Co 429 

Pennsylvania   railroad   shops  427 
relation  of  power,  supply  and 

demand,  diagrams  of 435 

relation    of,    to    stream    flow 

and  auxiliary  power 434 

study  of,  for  report  on  water 

power    679 

typical    factory 42S 

typical    railway 430 

Load  factor, 

definition  of 433 

effect  of  on  cost  of  power,  Ar- 
chibald       662 

effect   of   on   cost   of   steam- 
generated  electric  power  to 

the  consumer 669 

influence  of  on  operating  ex- 
penses     662 

literature  on 439 

Logan,  Utah,  tests  of  Leffel  tur- 
bines at 370 

Log    way 621 

at  Lower  Dam,  Minneapolis, 

Minn 62 1 

in    the    Chesuncook     timber 

dam   620 

Lombard  governor, 

operating  results  with 485 

details  of 481 

type    "R" 484 

type   "N" 480 

Lombard   hydraulic  relief  valves  496 
Lombard    relay   valve. .  .   483 


PACK 
Lombard-Replogle          mechanical 

governor    478, 479 

London  Hydraulic  Supply  Com- 
pany, maximum  days  of  pump- 
ing    429 

London      water      wheels,      float 

wheels    1 

London  Water  Works,  undershot 

wheel  used  in 14 

Losses, 

in  an  hydro-electric  plant. ...     26 

in    belts 30 

in\  machinery 23 

in   turbines 27,371 

Low  heads,  vertical  shaft  tur- 
bine for 509 

Low  water  flow,  effects  of 107 

Machine  factor,  definition  of....   433 

Machine,  ideally  perfect 23 

Machine  selection,  load  curve  in 

relation,  to 433 

Machinery,    losses    in 23 

Madison,  Wisconsin,  diagram  of 
fluctuations  of  monthly  rain- 
fall at 122 

Manchester,  England,  sharp  thun- 
der storm  peak 426 

Maps  of, 

average    annual    rainfall    in 

the  United  States 112-113 

average    annual     rainfall     in 

Wisconsin    115 

rainfall     conditions     in     the 

United    States,    July    16-17  118 
weekly  distribution  of  rain- 
fall in  Wisconsin 117 

Manufacturing  purposes,  losses  in 

utilization  of  energy  for 30 

Market  price  of  water  power....   663 
Masonry  dams, 

literature    on 597 

stability   of 586 

Mass    36 

Mass    diagram     showing     run-off 

from  Tochickon   Creek 639 

Mathon,    DeCour 5 

McCall's  Ferry  dam,  section  of . . .   592 
McCormick,    John    B 13,266 


Index. 


773 


PAGE 

McCormick   turbine, 267,    269 

test  of  a  57   inch 708 

test  of  a  51  inch 711 

test  of  a    39  inch 717 

Mechanical  governor, 

anti-racing,    Woodward 473 

Lombard-Replogle     478 

simple,    Woodward 472 

Mechanical  type  of  relay 471 

Merrill,  Wisconsin,  rainfall  above  129 
Merrimac  River  discharge, 

arranged      in      chronological 

order   172 

arranged  in  order  of  magni- 
tude        174 

Meter,  the  wheel  as  a 365 

Michigan    drainage    area 185 

Michigan  rivers, 

comparative    hydrographs    of 

various   186 

discharge    in    cubic   feet    per 
second  per  square  mile  of 

drainage  area 18<8 

Mississippi  Valley  Drainage,   hy- 
drographs   of 192 

Missouri  River,  variations  in  the 
cross-section    of,    near    Omaha, 

Neb 210 

Momentum,    exertion    of,    energy 

by 41 

Moore  bucket   274 

Morin,  tests  in  1838 359 

Morris  Company,  I.  P 252,  268 

diagram   of   double   Fourney- 

ron     turbine 253 

estimate  for  turbine  for  Mc- 

Call-Ferry  Power  Co 412 

graphical    diagram    of    rela- 
tions of  power  and  head. . .   413 
graphical  diagram  of  test  of 
wheel   of   The   Shawinigan 

Power  Company 382 

Shawinigan  Falls  turbine...   270 
Trenton    Falls   plant  of   The 
Utica  Gas  and  Electric  Co.  511 

Morris,  Elwood, 9 

first  systematic  tests  of  tur- 
bines in  U.  S.. .  .   359 


PAGE 
Morris   plant   of   Economy   Light 

and  Power  Co 572 

Motion, 

compound    37 

laws     of 36 

uniform    37 

uniformly  varied 37 

Motor    installation,     capital    cost 

and  annual  charge  on .....   657 

ordinary  efficiency  of 31 

Movable    crest    for    dam    at    Kil- 

bourn,   Wisconsin 608 

Movable  dams 100,  603 

at  McMechan,  W.  Va 603 

literature    on 622 

Mullin's   formula    (used   by   East 

India  engineers) 69 

Murphy,  E.  C.,  methods  of  current 

meter  computation 227 

Muskingum     River,     run-off    dia- 
gram of 156 

table  showing  relations  of 
rainfall  to  run-off  for  vari- 
ious  periods 156 


Necedah,  Wisconsin, 

hydrograph    of    the    Wiscon- 
sin River  at 96 

rainfall    above 129 

rating    curve    of    Wisconsin 

River  at 96 

Needle  nozzle,  Doble,  cross  section 

of   306 

Neshaminy    Creek, 167 

rainfall,  run-off  and  evapora- 
tion       754 

Nevada  Mining  and  Milling  Com- 
pany, plant  of 555 

New  American  turbine 257 

test  of  a  44  inch 714 

runner    of 260 

Newell,  F.  H.,  estimates  of  rela- 
tion of  rainfall  to  run,'-off 174 

Newton's  laws  of  motion 36,  38 

Niagara  Falls, 

estimate  of  the  cost  of  hydro- 
electric plant  at 643 


774 


Index. 


Niagara  Falls — Con.  PAGE 

first  power  at 15 

power    development 576 

water  power  at 22 

Niagara   Falls   Hydraulic    Power 
and    Manufacturing    Company 

255,  266 

Niagara  Falls  Paper  Company. . .  254 
Niagara   Falls    Power    Company, 
the  vertical  bearing  used  by  291 
double  horizontal  Leffel  tur- 
bine of  the 265 

tests  of  wheels  of 380 

Niagara  River,  hydrograph  of  dis- 
charge of 179 

Niagara  Falls  Water  Power  Com- 
pany      252 

Niagara  Fourneyron  turbine 290 

Nomenclature  for, 

governor    .calculations 447 

turbine    discussion 310 

Nora,  Chinese 1 

Northern    Hydro-Electric    Power 
Company,     hoists     for     tainter 

gates   for 606 

Northern  rivers,  monthly  rainfall 

and   run-off 165 

Nunn,  P.  N.,  turbine  tests  at  Lo- 
gan,   Utah 379 

O. 

Oberchain,  Matthew   and  John..  267 
Obstructions, 

effect  of  change  in 205 

effects  on  channel  grade,  and 

on  the  hydraulic   gradient  204 
Ogden  pipe  line,  experiments  on     60 
Ohio     Valley     drainage,     hydro- 
graphs    of 191 

Oliver  Power   Plant,   wheel   har- 
ness of 530 

Ontario      Hydro-Electric      Power 

Commission,  estimates  by 

648,  649,  654,  656,  657,  664 
Open  channels,  flow  in,  literature 

of   198 

Open  penstocks, 

application  of  method  to 465 

predetermination      of     speed 


Open  Penstocks — Con.  PAGE 

regulation    for    wheels    set 

in   461 

Operation,  economy  in 527 

Operating  expenses, 

effect  of  load  factor  on...,.   662 
estimate   of  for  various  pro- 
posed Canadian  plants....   654 
ratio  of  individual   items   to 

total    660 

Orifices, 

flow  of  water  through 01 

submerged  43 

Oscillatory    waves    in    long    pen- 
stock      451 

Outward  radial   flow   turbines...   244 

Overload    526 

Overshot  water  wheels 3,  243 

Laxy    14 

P. 

Pacific     Coast,     development     of 

wheels    on 275 

Paddle   wheels 241 

Paris     water     works,     undershot 

wheel  used  in 14 

Partial  load,  effect  of  on  cost  of 

power    651 

Partial    turbines 244 

Passaic  River, 

hydrographs    of 182-18S 

rainfall  on  drainage  area  of 

182-18a 

relations   of  rainfall  to   ruii'- 

off 182-183 

rim-off  diagrams  of 155 

Pel  ton, 

bucket    274 

tangential   water   wheel   run- 
ner       27d 

Water    Wheel    Company    275-276 

wheel     276, 307 

Penstock  velocity, 

change  of 453 

energy    required    to    change 

446-456 

Percolation,   literature   on 144 

Periods,  growing     15? 


Index. 


775 


Periods — Con.  PAGE 

replenishing    157 

storage    157 

Pcrkiomen    Creek,,. 167 

rainfall,  run-off  and  evapora- 
tion       75G 

Peshtigo  River  development,  pro- 
file of 574 

Philadelphia,    water    wheel    tests 

in  1860  at 360 

Pile  foundations  for  dams..   603,  608 

Piobert  and  Tardy 8 

Pipe> 

Chezy's    formula 60 

Darcy's    formula 60 

flow  of  water  in 59 

literature  on  flow  of  water  in     76 

losses   in  asphalt  coated 62 

Plant  capacity 525 

Plant  design,  study  of  for  report 

on  water  power 681 

Plant  of, 

Columbus  Power  Company..   546 
Hudson    River    Transmission 

Company   at   Spier's    Falls  546 
Nevada   Mining   and   Milling 

Company    555 

South  Bend  Electric  Company  546 
Sterling     Gas     and     Electric 

Company    537 

The   Concord    Electric    Com- 
pany       553 

The  Dolgeville  Electric  Light 

and  Power  Company 548 

The    Lake     Superior    Power 

Company    570 

The     Niagara     Falls     Paper 

Company    257 

The    Shawinigan   Water   and 

Power    Company 550 

Winnipeg    Electric    Railway 

Company    553 

York    Haven     Water    Power 

Company     537 

Plants, 

Located  in  dams 574 

with   concentrated   fall 564 

with  divided  fall 564 

with  head  race  only..  .   570 


PAGE 

Platt  Iron  Works  Company 

. .  .267,  268,  276,  295,  300,  301,  308 
characteristic  curves  of  a  Vic- 
tor  turbine 402-403 

graphical  diagram  of  test  of 
25  inch  Victor  high  pres- 
sure turbine 382 

relations  of  efficiency  to  dis- 
charge at  various  revolu- 
tions    405 

the  Snoqualmie  Falls  reac- 
tion turbine 272-273 

test  data  of  48  inch  turbine  704 

test  of  a  42  inch  turbine 715 

test  of  a  45  inch  turbine 712 

tests  of  a  36  inch  turbine 720 

tests  of  a  33  inch  turbine 723 

Poncelet's  wheel 4,  241 

Pondage, 

effect  of  limited,  on  the  power 

curve     624 

effect  of  on  power 624 

hydrograph  on  Fox  River 
showing  effect  of  Sunday 
shutdown  of  hydraulic 

plants    628 

hydrograph  showing  effect  of 

626 

study  of  for  report  on  water 

power    679 

Pondage  and  storage, 

analytical  method  for  calcu- 
lating    644 

Potential  energy, 20,  33 

development    of 19 

generation  of  power  from. ...     26 
Potomac  River, 

discharge  arranged  in  chronr 

ological    order 172 

discharge  arranged   in  order 

magnitude    174 

discharge,  velocity  and  area 

curve  of 232 

Power, 

actual  conditions  under 
which  same  is  furnished 
to  consumers  from  central 
stations  .  668 


776 


Index. 


Power — Con.  PAGE 

at  Kilbourn,  graphical  study 

of   .104 

charges  for  by  Cataract 
Power  and  Conduit  Co.  of 

Buffalo 670 

conversion  of 26 

development  of 

at  Niagara  Falls 576 

study    of    for    report    on 

water    power    680 

effect  of  on  pondage 624 

from    municipal    sub-station, 

estimated  cost  of 656 

literature    on 672 

measurment    of 375 

of  the  Kilbourn  wheels  un- 
der variations  in;  flow 106 

of  plant  as  influenced  by  var- 
iable head,  hydrograph 

showing    110 

of  plant,  effect  of  head  on . .   100 

of    steam 33 

of  stream  as  affected  by  flow     79 

of    turbine, 325 

expression    for 336 

of  homogeneous  design . .   341 

proportional  to  hi 8v>5 

of  water 33 

relation  of  to  head  in  a  12 
inch  Smith-McCormick  tur- 
bine    33G 

sale    of 666 

transmission  of 26 

utilization    of 26 

Power  and  diameter, 

graphical  relations  of  in  tur- 
bines of  homogeneous  de- 
sign    341 

of  various  American  turbines  342 
Power  and  energy,  literature  on..  39 
Power  and  speed  of  turbines, 

relations  of 347 

various  American 350 

Power  curve, 

effects    of    limited     pondage  624 

hydrograph  as  a 89 

Power,   head,   and    flow,    relation 
of   at   Three  Rivers,   Michigan  103 


PACK 

Power  hydrograph  at  Kilbourn  91 
Power  hydrograph  at  Sterling, 

Illinois    C25 

Power   losses   in   generation   and 

transmission  of  energy 27 

Power  plant  at  Turner's  Falls. . . .  514 
Power  station, 

and  dam,  relation  of 561 

study  of  site  of  for  report  on 

water  power 681 

Power  transmission, 

estimate    of    investment,    an- 
nual charges  and  costs.  . . .   656 

literature    on 673 

Precipitation, 

in    United    States,    types    of 

monthly   distribution 123 

relation  of  evaporation,  run- 
off and  temperature  to,  on 

Lake   Cochituate 140 

run-off,  evaporation  and  tem- 
perature, relations  on  Siid- 

bury    River    basin 151 

run-off,  evaporation  and  tem- 
perature,   relations    of    on 

Upper  Hudson  River 154 

variations  at  stations  closely 

adjoining    125 

Pressure,  exertion  of  energy  by. .  41 
Pressure  or  reaction  turbines.  . . .  244 
Price's  electric  current  meter. . . .  222 
Prime  movers,  possibilities  of. ...  528 

Prony  brake,  W.  O.  Weber 377 

Pumping  engine,  efficiency  of. ...  23 
Pumping  plant, 

at  Connorsville,  Indiana,  reg- 
ulation   of 441 

energy   losses   in   steam   and 
electric   25 

R. 
Raceways, 

of     Holyoke     Water     Power 

Company    56S 

of    Sterling    Hydraulic    Com- 
pany       567 

Racing     or     hunting     of     water 
wheels     ,        447 


Index. 


777 


PAGE 

Racing,  value  of 456 

Racks,  trash 536 

Rafter     and     Williams,      experi- 
ments   of. 65 

Rafter,  George  W., 

discussion  of  rain  fall 125 

discussion  of  Vermuele's  for- 
mula      148 

graphical  comparison  of  dis- 
charge  over   weirs 68,  69 

graphical    diagram    showing 
discharge  over  weirs  with 

irregular  crest 72-73 

report  to  the  Board  of  Engi- 
neers on   Deep   Waterways     65 

Railway  load  curve,  typical 430 

Rainfall, 

accuracy  of  records  of ........   122 

at  Merrill,  Wis ,120 

annual  at, 

Augusta,   Ga 120 

Cincinnati,   0 120 

Des  Moines,  Iowa 120 

Detroit,    Mich 120 

Helena,    Mont 120 

Little  Rock,  Ark 120 

Madison,     Wis 120 

Montgomery,  Ala 120 

Moorhead.    Minn 120 

New   Haven,  Conn 120 

Phoenix,    Ariz 120 

Sacremento,    Cal 120 

San  Antonio,  Texas 120 

Spokane,   Wash 120 

Tacoma,    Wash 120 

Topeka,    Kans 120 

Winnemucca,    Nev 120 

annual,   local   variations  and 

periodic   distribution   of 121 

conditions     in      the     United 

States    118 

data,  availability  of 87 

disposal    of 133 

distribution  of Ill 

in    United     States,   types    of 
monthly  distribution  of...   123 

literature  on 130 

literature  on   disposal  of..    .   144 


Rainfall — Con.  PAGE 

maps   and   records,   accuracy 

of 122 

monthly  mean   at, 

Augusta,  Ga 127 

Cincinnati,   0 127 

Des  Moints,  Iowa. 127 

Detroit,  Mich... 127 

Helena,  Mont 127 

Little  Rock,  Ark 127 

Montgomery,    Ala 127 

Moorhead,    Minn 127 

New   Haven,  Conn 127 

Sacramento,    Cal 127 

San  Antonio,  Tex 127 

Spokane,    Wash 127 

Tacoma,    Wrash 127 

Topeka,  Kans 127 

Tucson,  Ariz 127 

various  points  in  United 

States    127 

Winnemucca,  Nev 127 

observations,  accuracy  in...     126 
on  the  drainage  area  of  the 

Wisconsin  river 129 

records,  value  of  extended..   124 
relations  of  annual  to  run  off  177 

study    of, Ill 

as   affecting   run-off 126 

for      report      on     water 

power 677 

rate  or  intensity  of 133 

relation  to  river  discharge..   745 
run-off   and    evaporation,    for 

various   periods 750 

variations      of      at     stations 

closely    adjoining 125 

Rainfall  and  Altitude 124 

Rainfall  to  run-off 

monthly  relation  of 162 

on  southern  rivers 166 

on   Northern   rivers 165 

on    Sudbury   River    for   each 

period  of  the  water  year. .   161 
on   upper   Hudson   River   for 
each   period   of   the   water 

year  160 

relations     between     monthly 
depth  of 161 


778 


Index. 


Rainfall  to  run-off — Con.  PAGE 

relations     between,     on     the 

Passaic   river 182-183 

relation   of,   for  various  per- 
iods    on    the     Connecticut 

River 159 

relations  of,  for  various  per- 
iods on  the  Hudson  River  158 
relations  of,  on  the  Hudson 
and     Genesee     River,     dia- 
gram    of 155 

relation  of  periodic 159 

Rating  curve, 

changes     in     head     due     to 
changes  in  cross  section..     96 

current    meter 221 

for   Wallkill    River,    ice   and 

open  conditions 217 

for  Wisconsin   River  at  Kil- 

bourn,    Wisconsin 209 

influence  of  stream  cross  sec- 
tion   on 95 

Rating  or  discharge  curve 95 

Rating  station  for  current  meters, 

Denver,    Colorado 223 

Reaction  and  impulse  turbines..   311 

relative  advantages  of 245 

Reaction  turbine, 237,  239,  316 

American    type 256 

arrangement  of 500 

condition  of  operation  of....   245 

diagrams     of 240 

economical  operation  of 31$ 

friction  of 318 

general   conditions   of  opera- 
tion       500 

graphical  relation  of  energy 

and  velocity  in. . 321 

graphical  relation  of  velocity 

and  energy  in  flow  through  320 
minimum    residual     velocity 

of  water  in  leaving  buckets  319 
necessary  submergence  of...   501 

path  of  jet 317 

relative  velocity  of  the  bucket    318 
residual     velocity     of    water 

from    31S 

Snoqualmie   Falls 272,273 


PAGE: 

Register   gates 301,  301 

diagram      showing      eddying 

caused    by 305- 

Regulation  of  impulse  wheels...  452: 
Regulation  of  turbines,  compara- 
tive        487 

Reinforced  concrete  dams,  litera- 
ture on 601 

Relay, 

hydraulic  type  of 471 

mechanical  type  of 471 

Relay  Valve,  Lombard 483" 

Relief    valves, 495-498- 

Lombard    hydraulic 49ft 

on  end  of  penstock 49f> 

Sturgess  49S 

Rennie    3- 

Replenishing    period 15T 

Report   of   water   power,   general 

outline    of 683 

Resistance  and  speed,  relation  of  44ft 
Retardation  of  water  in  penstock  690 

of  on  gradient 201 

Rising  or  falling  stream,   effects 

Risler,   M.   E.,   estimate   of   daily 

consumption  of  water  by  differ- 

erent  kinds  of  crops 135 

Rivers, 

comparative    hydrograph     of 

various  in   Michigan 18f> 

hydrographs  of, 

Alcovy   River 190 

Bear  River,  Utah 19S 

Clear    Creek 192 

Chittenango   Creek 191 

Coosa   River 19ft 

Grand    River    at    Grand 

Rapids    191 

Hood  River 193 

Iron    River 193" 

Kalawa  River 193 

Kennebec  River 19ft 

Kern  River 193 

Licking    River 191 

Meramec   River 192 

Niobrara  River 192 

Otter    Creek..  .   192 


Index. 


779 


Rivers,  hydrographs  of — Con.       PAGE 

Perkiomen    Creek 191 

Rio   Grande  River 192 

Salt    River 192 

San  Gabriel  River 193 

Seneca   River 191 

Spokane  River 193 

Tennessee  River 191 

Walker  River 19;! 

Wisconsin    River   at   Ne- 

cedah,    Wis 192 

Yadkin    River 190 

Yellowstone   River 192 

monthly    discharges    in    cub. 
ft.  per  sec.  per  square  mile, 

Ausable   River 183 

Grand    River    at    Grand 

Rapids    188 

Grand  River  at  Lansing, 

Mich 1S8 

Kalamazoo    River 1 88 

Manistee  River 188 

Muskegon   River 188 

St.    Joseph   River 18S 

Thunder  Bay  River 188 

White  River 188 

relation  of  rainfall  and  run- 
off  on 165 

Reek-fill  dams,  literature  on 597 

Rockford,  Illinois, 

details  of  head  gates  for  Mr. 

Wait    Talcott 610 

flashboards  and  supports  at. .   609 
Rock  River, 

at  Rockton,  Illinois 165 

comparison  of  mean  monthly 

flow  with  Wisconsin  River  178 
Rodney  Hunt  Machine  Company 

267-268 

Rome,  water  wheels  in 14 

Rotary  converters,  losses  in 29 

Rotation  of  water  wheels,  direc- 
tion   of 289 

Rou6   a  Cuves 8 

Rou6  Volant 8 

Runner, 

details    of 28C 

its  material  and  manufacture  2j84 
Improved  New  American....  261 


Runner — Con.  PAGE 

of  Girard  turbine 280 

Run-off    (see  also  Stream  Flow), 

relations  between  monthly 
depth  164 

study  of  for  report  on  water 
power  676 

and  rainfall,  monthly  rela- 
tion of 162 

and  rainfall,  monthly  rela- 
tions on  Southern  Rivers..  16(5 

and  rainfall,  monthly  rela- 
tions of  on  Northern  Rivers  left 

diagrams 

of   Hudson   and   Genesee 

River    155 

of  the  Muskingum  River  156 
of  the  Passaic  River....  155 

effects  of  area  on 179 

effects  of  geological  condi- 
tions on 177 

effects  of  rainfall  on 126 

influence  of  storage  on  the 
distribution,  of 179 

influen.ce  of  various  factors 
on 14S 

mean  annual  of  the  rivers  of 
the  U.  S 152-153 

precipitation,  evaporation  and 
temperature,  relations  of 
on  Upper  Hudson  River..  154 

precipitation,  run-off  and  tem- 
perature, on  Sudbury  River 
basin,  relations  of 151 

rainfall,  and  evaporation, 
for  various  periods 750 

relation    of   periodic   rainfall 
•      to   159 

relation  of  annual  rainfall  to 

175-177 

relation  to  precipitation,  eva- 
poration and  temperature 
on  Lake  Cochituate..  .  149 


S. 

Sale  of  power, 646-666 

an  equitable  basis  for 669 

literature  on?. .  .   673 


Index. 


PAGE 

Saline    River,    cross    section    at 

guaging    station 225 

Samson     turbine, 265 

section  and  plan  of 263 

test  of  a  56  inch. . : 709 

test  of  a  45  inch 713 

top  and  outside  view  of  run- 
ner of 261 

characteristic  curve  of  a  45 

inch     410-411 

Schiele    turbine 239 

Science  of  hydraulics 40 

Scotch  turbine 7,  239 

Seattle  and  Tacoma  Power  Com- 
pany,  The 268 

Sewall's    Falls,   vertical   turbines 

for 512 

Shafting,  efficiency  of 24 

use  of 533 

Shawinigan  Falls  turbine...   268,  270 

runner    of 271 

efficiency  and  discharge  dia- 
gram of 381 

Shawinigan)   Water     and     Power 

Company,  plant  of 550 

Shock,  due  to  sudden  changes  in 

velocity    449 

Shutter,    automatic    drop    at    Ba- 

tavia,    India 610 

Site    of   dam   for    power   station, 
study     of     for     report     on. 

water  power ' 681 

Slope,  estimates  of  flow  from 210 

Smeaton's  experiments  on  water 

wheels    357 

Smith,  Hamilton,  Jr's.,  coefficients 

of  discharge  for  weirs 74 

Smith-McCormick  turbine, 

relations  of  head  to  discharge 

of   334 

relations  of  power  to  head  in, 

a  12  inch 336 

runner-    of 267 

Smith    turbine 267 

S.  Morgan  Smith  Company, 267 

curve  of  relations  of  dis- 
charge and  speed  from  ac- 
tual tests. . .  .393 


S.   Morgan   Smith  Co. — Con.  PAGE 

curve  of  turbine  from  actual 

t(ysts     399 

relation  of  efficiency  to  speed 

in  a  33  inch  wheel 395 

relation  of  power  ami  speed 
from  actual  turbine  tests..   396 

test  of  a  33  inch  turbine 717 

tests  of  a  33  inch  special  tur- 
bine      7.21 

turbine,    relations    of    speed 

and  efficiency  in 329 

turbines  for  Contcord  Electric 

Co 513 

two  pairs  of  turbine  units  in 

tandem   519 

Snoqualmie    Falls    reaction    tur- 
bine         272,    273 

diagram  showing  relation  of 

gate  guides  and  buckets..   303 
diagram  showing  rigging  for 
opening       and       operating 

.  gates    : 303 

thrust  bearing  of 296 

Solar  energy 19,  20 

South    Bend   Electric    Company's 

plant   546 

Southern  Wisconsin  Power  Com- 
pany, 
dam    with.. movable   crest    at 

Kilbourn,    Wis 60S 

head  gate  hoists  for 617 

Kilbourn    plant    of 521-569 

preliminary  study  of  dam  for  585 
Southwestern  Missouri  Light  Co., 

harness  and  sheaves  of. ...   533 
Special   New   American   runner. .   261 

Specifications  for  governor 467 

Specific  speed  or  system  curve  of 

turbines    349 

Speed, 

economical     speed      of     any 

wheel    329 

relation)    necessary    for    con- 
stant       442 

relation  of  turbine  speed   to 

diameter  and  head 324 

Speed   and    discharge  of   various 
American   turbines. .  ....   34»J 


Index. 


78i 


PAGE 

Speed    and    power    of    turbines, 

relation  of 347 

Speed  and  power,  selection  of  a 

turbine  for,  under  fixed  heads. .  387 
Speed  and  power  of  various  Am- 
erican   turbiixes 350 

Speed  and  resistance,  relation  of  440 
Speed,    cp    and   horse    power,   ex- 
perimental curve  showing  rela- 
tion   of 415 

Speed  of  rotation,  measurements 

of   373 

Speed    of    turbines,    relation    of 

discharge  to 345 

Speed  records  from  Hudson,  River 

Power  Transmission  Co 486 

Speed  regulation, 

detailed  analysis  of 688 

for  plant  with  open  penstock, 

predetermination  of 461 

plant  with  closed  penstock..   462 

plant  with   stand  pipe 463 

graphical   analysis   of '.  693 

influences  opposing 453 

Speed  relations,  graphical  expres- 
sion, of 329,331 

Special  New  American  turbine. . .   257 
Spier's    Falls    plant    of    Hudson 
River  Power  Transmission  Co.  546 

Spouting  velocities  of  water 741 

Stability  of  masonry  dams,  litera- 
ture on 505 

Stand  pipe, 453 

discussion   of    relative   speed 

regulation    696 

fluctuation  of  head   in 699 

numerical  problem 466 

predetermination     of     speed 

regulation  with 463 

St  Clair  River, 

drainage   and   guage   heights 

on     200 

hydrograph    of    discharge    of 

the   180 

variations  in  velocity  in  the 

cross  section  of 211 

Steam      and      electric     pumping 
plant,  energy  losses  in 25 


PAGE 

Steam    engine,    efficiency   of 24 

Steam  plant,  capital  cost  and  an- 
nual cost  of  per  brake  H.  P...   664 

Steam    power 33 

Steam  power  plant,  energy  losses 

in   24 

Steel  dams,  literature  on 601 

Sterling   Gas   and   Electric    Com- 
pany   plant 537 

Hydraulic  Company,  race- 
ways of 567 

power    hydrograph.... 625 

tainter  gates  in  U.  S.  dam  at  604 
timber  fishway  in  dam  at...   619 
St.     Lawrence     drainage,     hydro- 
graphs  of 179, 191 

St.  Mary's  River,  hydrographs  of 

discharge  of  the 180 

Storage,    624 

calculations   for 635,   636 

diagram     showing    effect    of 

large   storage   capacity 633 

effects  of  limited 629 

effect   of   maximum 635 

influence    of   on    distribution 

of    run-off 179 

limited,  effect  on  low  water 

flow  at  Kilbourn 629 

literature  on 645 

study  of  for  report  on  water 

power 67$ 

period    of 157 

Stout,  Mills  and  Temple 13,  25G 

Strabo,  reference  on  water  wheels     14 
Stream  flow, 

broad  knowledge  of  neces- 
sary for  water  power  pur- 
poses    SO 

estimates   of 169 

factors    of 79 

graphical     determination    of, 

from  measurements 230 

literature    on 19S 

maximum 16:> 

measurements,  necessity  of. .   21S 

relation  of  load  curve  to 434 

value   of   single  observations     80 


782 


Index. 


Stream  flow — Con.  PAGE 

variation     of    from     year   to 

year     82 

Stream  guaging, 

application    of 231 

cable  station  for 228 

Stream,  study  of  from  its  hydro- 
graphs 181 

Sturgess     governor,    test     results 

with    491 

hydraulic  governor 486 

Type  N,  section  of 489 

relief  valves 498 

Submerged  orifices 43 

Submergence  of  reaction  wheel..   501 
Sub-stations,    estimated    cost    of 

power  from 65C 

Sudbury  River,  rainfall  and  run- 
off  of   for   each   period   of   the 

water   year 161 

Sudden  enlargements 42 

Swain  turbine 13,  249 

test  of  a  36  inch 718 

Switchboard,  control  of  governors 
from    m   492 


Tailwater    curve 9.3 

Tainter  Gates, 

for  Morris  Plant  of  Economy 

Light  and  Power  Co 605 

in   U.   S.   dams  at  Appleton, 

Wis 607 

in  U.  S.  dam  at  Sterling,  Il- 
linois     604 

Talladega  Creek    166 

Tangential  wheels    (see  also  Im- 
pulse Wheels) 241 

angle  of  discharge  from  buck- 
ets   of 3H 

Atkin's  wheel  and  case...,.  273 

early  forms  of g 

effect  of  angle   of   discharge 

on   efficiency 315 

efficiency    of 247 

maximum    work... 314 

path  of  jet 316 

runners  of 284 


Tangential    wheels — Con.  PAGE 
Telluride  double,  2,000  H.  P.  275 
Tate,  Professor  Thomas,  on  evap- 
oration       141 

Taylor,   J.   W.,  turbine 300 

Telluride  double  tangential  wheel  275 
Telluride  transmission  plant,  the  276 
Temperature  an/i  evaporation,  re- 
lations of  on  Lake  Cochituate 

basin   150 

Temperature,  precipitation,  run- 
off and  evaporation,  rela- 
tions of, 

on  Sudbury  River  basin 151 

on  the  Upper  Hudson  River  154 

on  Lake  Cochituate 149 

Test  data  of  turbine  water  wheels  703 

Testing  turbines 355 

purpose  of 370 

flumes  for  at  Holyoke 364 

machinery  for,  importance  of  355 

by  James   Emerson. 361 

early    methods 359 

literature    on 383 

plan     of    apparatus     for    by 

James  B.  Francis 374 

illustration    of    methods    and 

apparatus 378 

Test   results    with   Sturgess   gov- 
ernor       491 

Tests, 

curve  showing  discharge  and 

speed  of  wheel  from  actual  398 
factors  that  influence  the  re- 
sults   of 371 

of  water  wheels, 

at  Philadelphia  in  1860. .   360 
by  Messrs.  Samuel  Weber 

and  T.'  G.  Ellis 362 

in  place 379 

the  value  of 369 

Thermal    energy 20 

Thermal    units,    British 32 

Thompson's  turbine 239 

Three-halves  powers  of  numbers.   742 
Three  Rivers,  Michigan,  variation 

in  power  at 103 

Thrust    bearing    at    Snoqualmie 
Falls    .  .  295 


Index. 


PAGE 

Thunder  Bay  River 165 

Thurso,  J.  W 279 

Tidal  mill..... 14 

Timber  dam, 

at  Janesville 582 

at   Sewell's   Falls 594 

of  the  Montana  Power  Com- 
pany, near   Butte 593 

Timber  fishway, 

of  Fish  Commission  State  of 

Wisconsin    619 

in  dam  at  Sterling,  Illinois..  619 

Tohickon    Creek 167 

diagram  showing  annual  run- 
off from 638 

mass  curve  of  run-off  of 639 

monthly       discharge       from 

drainage  area  of 643 

monthly  rainfall  in  inches  on 

drainage  area  of 643 

rainfall,  run-off  and  evapora- 
tion      757 

Topographical  condition, 

relation  of  run-off  to 175 

study  of  for  report  on  water 

power    677 

Traction    purposes,    transmission 

of   power   for 26 

Trade    Dollar    Mining    Company, 

power   plant   of 532 

Transformation  of  energy 23-33 

Transformers,  losses  in 29 

Transmission  of  energy 23 

losses  in 27 

for   traction   purposes 26 

literature  on 673 

Transverse  curves  of  mean  veloc- 
ity in  stream  cross  sections...   211 

Trash   racks 53C 

Tremont-Fourneyron  wheel, 

characteristic  curve  of 409 

diagram    of 21 

efficiency    of 247 

guides  and  buckets  of 251 

Trenton    Falls,    N.    Y.,    plan    of 

power   development  at 575 

Tub  wheel . .  8 


PAGE 
Turbines, 

American,    Francis 11 

Cadiats,  Fourneyron,  Fran- 
cis, Girard  Current,  Hen- 
schel,  Jonval,  Schiele, 

Scotch,    Thompson's 239 

advantages  of 9 

arrangement  of, 

horizontal    504 

reaction    500 

vertical  shaft 501 

axial    flow 244 

bearings  of, 

horizontal    292 

vertical  239 

calculation   of, 

a   more   exact    graphical 

method   for 396 

graphical     method,      effi- 
ciency   and    speed    at 
various  heads  and  gates  395 
diagram      of      estimated 

power  at  various  heads  397 
to  estimate  operating  re- 
sults   under    one    head 
from    test    results    at 

another   head 389 

to  estimate  results  of  one 
diameter  from  tests  of 

another    391 

capacity  of, 

power  and  speed  of  a  40" 
wheel   under   16'   head  260 

characteristic  curve  of 400 

classification  of 243,506 

complete     244 

connection  of,  to  load 531 

conditions    of    operation     of 

245,384 

constants   of 310,  351 

design  of,  first  principles. . .  .   311 
details   and   appurtenances..  284 

development    of 4 

in   Europe 277 

in   United    States.. 24S 

discharge, 

measurement    of..  .   372 


784 


Index. 


Turbines — Con.  PAGE 

at  fixed  gate  opening 332 

fundamental  ideas  of 5 

gates   of 290 

history    of 8,9 

horizontal    244 

horizontal,  multiple  tandem.   517 

hydraulics  of,   practical o09 

impulse    or    action^ 244 

installations  of, 

horizontal    513 

tandem    529 

vertical 507,  510 

inward  radial  flow 244 

limit    244 

literature    on 353 

mixed    flow 244 

number  of,  effect  on  head  and 

power    108 

partial     244 

outward  radial  flow 244 

power  of  modern,  increase  in     13 

power    of 335 

practice,  modern   changes  in     13 

radial    flow 244 

reaction,  or  pressure 244 

regulation,    comparative 487 

relations    321 

of  discharge  to  diameter 

in  various  wheels 339 

of  diameter  and  speed..  326 
of  discharge  to  diameter  337 
of  efficiency  and  speed  of 

33"  turbine,  graphical.   395 
of  efficiency  and  speed  of 

a  48"  Victor,  curve  of  322 
of      <p       and      discharge 
(graphical)  at  full  gate 
for  various  wheels....   333 
of  head  to  discharge  of  a 

12"   Smith-McCormick.   331 
homogeneous    series,    di- 
ameter   and    speed 326 

homogeneous  series,  pow- 
er and  diameter..   340,341 
to    estimate    results    for 
variable      head      from 
tests  under  fixed  head  393 
of  power  to  diameter  uh- 


Turbines — Con.  PAGE 
der  unit  head  (graphi- 
cal)       344 

of    power    and    speed    of 

a  33"  wheel 396 

of  power  and  speed,  48" 

Victor     (graphical)...   323 
of  power  and  head,  I.  P. 

Morris    Co 415 

of  speed  to  diameter  and 

head    324 

of  speed  to  discharge...   345^ 
of  speed  to  discharge  for 
a  12"  Smith-McCormick  3'tt 

of  speed  and  power 347 

runners  of, 

built  up 284 

cost    281 

details  of 28G 

how  made 284 

Shawinigan   Falls 272 

Scotch  7 

selection  of 38 1 

basis    for. .-. 385- 

for   speed   and   power   to 
work     under     a     fixed 

head 38T 

uniform  head  and  power  287 

Shawinigan  Falls 270 

speed,  increase  of 259 

speed    relations    of 330 

support  of 53* 

Swain    13 

testing  of 355- 

tests, 

by  James  Emerson 361 

literature  on 383" 

methods    and    apparatus 

for    , 378" 

plan  of  apparatus  for,  by 

Francis     374 

value  of 270,369 

vertical     244 

vertical  and  horizontal 244 

vertical  shaft  for  low  heads.  .  oOO 
Unwin's  estimate  of  losses  in  26" 
units,  two  pairs  in;  tandem 

519, 523 
Turner's  Falls  power  plant 514 


Index. 


785 


PAGE 

Tutton's    formula 62 

Tweeddale's  report  to  the  Kansas 

State   Board  of  Agriculture ...  136 

Tyler,    Benjamin 6 

Tympanum,   Egyptian 14 

U. 

Umbrella  covering, 

tests  of 729 

to   prevent   vortices 725 

Unbalanced  wheels 524 

Undershot  wheels 2 

early     application     to     mine 

drainage 16 

Uniform    motion 37 

Uniform   speed,  value  of 444 

Uniform   varied   motion 37 

United  States, 

annual  evaporation  in  the  138-139 
average  rainfall  of,  map  112-113 
comparative          hydrographs 
from  different  hydrological 

divisions    189 

development  of  water  power 

in   14 

first  wheel  in 9 

mean    annual    run-off   of   the 

rivers  of 152-153 

rainfall    conditions    in,    July 

16th  and   17th 118 

Units  of,  energy 32 

heat 3:> 

potential    energy 34 

University  of  Wisconsin, 

experiments   on    12"   S.    Mor- 
gan-Smith wheel 329 

experiments     on     submerged 

orifices  at 43 

Unwin,    Professor . . . 26 

Upadachee    River 166 

Utica  Gas  and  Electric  Co.,  Tren- 
ton Falls  plant  of 511 

V. 

Valves,   relief 498 

Velocities,  position  of  mean  and 
maximum  in  a  vertical  plane 
under  ice .- 217 

48 


Velocity,  PAGE 

changes   of  penstock. .......   453 

effects  of  ice  covering  on  dis- 
tribution,   of.. , ...   215 

energy    required    to    change 

penstock 446,  456 

measurements  of  flow  by  the 

determination  of. 221 

relative,  of  the  bucket  in  re- 
action wheels. 318 

residual,    in   reaction   wheels  318 
shock  due  to  sudden  changes 

in 449 

variations    in   the   cross   sec- 
tion of  a  stream. 210 

Velocity  curves, 

for    open    and    ice    covered 
streams,  comparative  mean 

vertical 216 

ideal   vertical 213 

of  Potomac  River. .. . ...   232 

Velocity  head ;..,...     -It 

Vermuele,  C.  C. 148 

formula  for  the  relation  be- 
tween annual   evaporation, 
precipitation  and  run-off. .   148 
Vertical     Geylin-Jonval     turbine, 

diagram    of 251 

Vertical  turbine, 

arrangement  of 501 

for   low   heads 509 

for    Sewall's    Falls... 512 

bearings  of 289 

Vertical  thrust  or  hanging  bear- 
ing of  The  Niagara  Falls  Power 

Co 293 

Vertical   turbines,   some   installa- 
tions of 507 

Vertical    turbines  and   their   con- 
nection     .........   507 

Vertical  turbines  in  series,  some 

installations  of 510 

Vertical   suspension,  ball   bearing  291 
Vertical   suspension    oil   pressure 

bearing 292 

Vertical      velocity      curves,      in 

streams 211,  213,  214,  215 

Victor  turbine, 

characteristic  curves  of.  .402-405 


Index. 


Victor  turbine— Con. 

efficiency-speed  curve  of  a  48"  322 
relation  of  efficiency  to  the 

number  of  revolutions 405 

runner    of 267,268 

teats  of, 

data  of  a  48* 704 

test  of  a  45" 712 

of  a  42" 713 

•f  *36" 720 

of  a  33" 723 

VitruvUw'   description   of    water 

wheels    14 

Volt  33 

Volt,  coulomb,  equivalents  of 34 

Vortices,  effect  of  an  umbrella  up- 
on the  formation  of . .  72  tf 


W. 

River,  rating  curve  for  217 
Warren.  H.  B.,  ou  predetermina- 
tion of  spaed  regulation 462 

Waste  of  energy,  none  in  nature    20 
Water, 

circulation  of 20 

evaporation  of 20 

Water   hammer 685 

due  to  sudden  changes  in  ve- 
locity    449 

Water  power 33-79 

chronological  development  of    15 

sort  of  development 647 

development  in  the  U.  S 14 

market  price  of 663 

sources  of 79 

Water  power  development, 

examples   of 537 

financial  consideration  of...  646 

history  of 1-14-16 

investigation  of 675 

purposes  of 646 

relation  of  capacity  to  cost. .  648 

classification  of  types 562 

costs  of  various, 

American $50 

Canadian    $49 

Foreign    651 

Water  power  property,  value  of.  671 


PAGE 

Water  power  purposes,  dams  for  580 
Water  supplied  to  wheel,  effect  of 

slow  acceleration  on 455 

wheels  (.see  also  Turbines)   237 

Barker's   Mill 5 

breast    3 

Chinese  Nora 1 

classification  of L10.7 

current   1 

early  types  of 1 

float  1-3 

horizontal,  some  installations 

of   

installation  of  ta.ndem W 

Laxy  overshot  ou  Isle  of  Man     14 

overshot I,  M3 

Poncelet  4 

Roue*  a  Cuves 8 

Rou6  Volant 8 

Smeaton's  experiments  on.  .  .   :r>7 

testing    of 3  "HI 

tests  at  Philadelphia  in,  IS- 

tub 8 

undershot 2 

use  of 241 

wry  fly 6 

Water     wheel     governors      t  see 

Governors)    470-735 

problem   of 445 

types  of 470 

Water  year,  the MR 

rainfall    and    runoff    of    the 
Hudson     River     for     each 

period  of 1*0 

rainfall   and    run-off    of   the 
Sudbury    River    for    each 

period  of 161 

rainfall  and  run-off  of  vari- 
ous rivers 7o< 

Waters,  W.  A.,  graphical  analysis 

as  proposed  by 412 

Watt,  the  equivalents  of 

Weber,  Samuel  13 

and  T.  O.  Ellis,  turbine  tests 

by 

Weber,  W.  a, 

plan  of  brake  wheel 576 

plan  of  prony  brake 377 


Index. 


787 


PAGE 

Weekly     rainfall     in     Wisconsin, 

distribution  of 117 

Weight,  exertion  of  energy  by. .     41 
Weights     of     water,     equivalent 

measures  and 740 

Weirs, 

coefficients 65  et  seq. 

formulas  for 64 

measurements  of  flow  by 219 

comparative  discharge  over  68-69 
comparative    discharge    with 

irregular  crest 72-73 

flow  over 64 

literature   on    flow   of   water 

over  77 

Wellmari-Seaver-Morgan        C  o  m- 

pany 299-300 

characteristic    curve    of    51" 

wheel    408 

Western  drainage,  hydrograph  of  193 
Wheeler,  L.  L., 

design  of  fish  way  by 614 

tainter  gates  designed  by...   606 
Wheel    harness   of   Oliver    power 

plant  530 

Wheel    pit 535 

Wheels   (see  Turbines), 

Atkins'  wheel  and  case 273 

effects  of  number  on  head  and 

power    108 

gravity    237 

impulse    237-301-313 

other  American 266 

reaction    237 

Whitlaw,    James 6 

Wicket    gate 300-301 

diagram  showing  condition  of 
flow  through  open  and  par- 
tially closed 304 

Winnipeg  Electric  Railway  Com- 
pany, plant  of 553 

Wisconsin, 

diagram  of  fluctuations  of 
monthly  rainfall  at  Madi- 


Wisconsin — Con.  PAGE 

son     122 

distribution    of    average    an- 
nual rainfall  in 116 

distribution    of   total    annual 

rainfall  in lltJ 

distribution   of   weekly   rain- 
fall in 117 

maps   of   annual    rainfall   in 

114-115 
rainfall  on  drainage  area  of 

Wisconsin  River 129 

Wisconsin  River, 

comparative   flow    of 85 

comparison  of  mean  monthly 

flow   with   Rock  River 173 

drainage   area   of 84 

hydrograph       at       Kilbourn, 
based    on    observations    at 

Necedah   86 

hydrograph  in  1904 81 

monthly  rainfall  and  run-off  165 
rainfall  on  the  drainage  area 

of   129 

rating  curve  at  Kilbourn . . .   209 
rating  curve  at  Necedah ....     96 
relations  of  coefficient  to  hy- 
draulic   radius 199 

relations  of  gauge  heights  at 

various  stations  on 206 

Wood,  R.   D.,  and  Company 254 

Geylin-Jonval   turbine 266 

Wood  stave  pipe  friction  losses..     63 
Woodward   governors, 

compensating    474 

details  and  applications  of. .  477 

standard 471 

Work 32 

Wry  fly  wheel 6 


Y. 

York  Haven  Water  Power  Com- 
pany,   plant    of .537 


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